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APTITUDE MATERIAL

QUANTITATIVE AND REASONING APTITUDE

Prepared By : R.V.Dinesh.



CONTENTS

QUANTITATIVE APTITUDE:

1. NUMBER SYSTEM.

2. AVERAGES.

3. RATIO & PROPORTION.

4. PROBLEMS ON AGES.

5. PARTNERSHIP.

6. PERCENTAGES.

7. PROFIT, LOSS & DISCOUNT.

8. TIME & WORK.

9. SIMPLE & COMPOUND INTEREST.

10. TIME, SPEED, DISTANCE & TRAINS.

11. BOATS & STREAMS.

12. PERMUTATION & COMBINATIONS.

13. PROBABILITY.

14. CALENDER.

15. CLOCKS.

REASONING APTITUDE:

1. NUMBER & LETTER SERIES.

2. COADING & DECOADING.

3. DIRECTION SENSE.

4. BLOOD RELATIONS.

5. SEATING ARRANGEMENTS.



NUMBER SYSTEM, LCM HCF & SIMPLIFICATION.

NUMBERS

NATURAL NUMBERS: All counting numbers are called natural numbers. They are

also called as positive integers.

Ex) 1,2,3,4,5,…………..

WHOLE NUMBERS: All counting numbers together with zero are called whole

numbers.

Ex) 0,1,2,3,4,5,…………

INTEGERS: All natural numbers, zero & negatives of counting numbers are

called

Integers.

Ex) -3,-2,-1,0,1,2,3,……….

PRIME NUMBERS: A number greater than 1, which is divided by itself other than

one.

Ex) 2,3,5,7,11,………..

COMPOSITE NUMBERS: Numbers greater than 1, which are not prime are called

composite numbers.

Ex) 4,6,8,9,10,12,………..

i.1 is neither prime nor composite.

ii.2 is the only prime number and it is the least prime number.

iii.Product of any two prime number is always a composite number.

1. Find the sum of the first 50 natural numbers?

2. Find the sum of all odd numbers up to 100?

3. What is the sum of all natural numbers from 51 to 100?

4. A child saves Rs 1 in the month of Jan, Rs 8 in feb, Rs 27 in march, Rs 64 in

April and so on. How much will he save at the end of the year?



LCM & HCF

For any two numbers x, y, find LCM and HCF. Then the product of LCM and HCF of

that numbers is equal to the product of that numbers.

LCM * HCF = X * Y

1. Find the HCF of 90, 120?

2. Find the HCF of 18, 24, 30?

3. Find the HCF of 2923, 3239?

4. Find the HCF of 210, 385, 735?

5. The LCM & HCF of two numbers are 210 & 2 respectively. If one of the

numbers is 10, find the other number?

6. The LCM of 16, 24, 36, 54?

7. Find the LCM of 10, 20, 30, 40, 50, 60?

8. The product of two numbers is 7200. If their HCF is 20, what will be the

LCM?

9. Find the least number exactly divisible by 12, 15, 20, 27?

10. Find the number which when divided by 6, 7, 8, 9, 12 leaves the same

remainder 1 in each case?

11. Two alarm clocks ring their alarms at regular intervals of 50 sec and 48 sec.

if they first beep together at 12noon, at what time will they beep again for

the first time.

a. 12.10PM b. 12.20PM c.12.12PM d.12.11PM

12. Four bells toll together at 9.00am. They toll after 7, 8, 11 and 12sec

respectively. How many times will glow together again in the next three

hours? a. 3 b.4 c. 5

d. 6

13. At Ashok pillar crossing, three consecutive traffic lights change after 36, 42

and 72sec respectively. If the lights are first switched on at 9.00am sharp, at

what time will they change simultaneously?

a. 9:08:04 b. 9:08:04 c. 9:08:44 d. none



SIMPLIFICATION

1. Find 15.72 * 15.72 - 5.72 * 5.72

15.72 + 5.72

2. Find 3.457*3.457 - 2.543* 2.543

3.457-2.543

3. Find 1.5^3+4.7^3+3.83^3 - 3*1.5*4.7*3.8

1.5^2+4.7^2+3.8^2 - 1.5*4.7 – 4.7*3.8 – 3.8*1.5

4. Find (0.472)^3 + (0.528)^3

0.472*0.472 – 0.472 * 0.528 + 0.528*0.528

5. Find (842 + 123)^2 + (842 - 123)^2

(842*842) + (123*123)

6. Find (469 + 174)^2 - (469 - 174)^2

(469*174)

7. Find 25+[16-{12+(4+12-8)}]

7+ {4 – ( 6-2)}

8. Find (6+6+6+6)/6

4+4+4+4/4

9. Find 128 / 16 *x – 7 * 2 = 1 Find X.

7^2 - 8 * 6 +X^2

10. Find X 0.39 * 0.39 + 0.125 * 0.125

0.375 – 0.125



PROBLEMS ON AVERAGES

1. In the first 10 overs of a cricket game, the run rate was only 3.2. What should

be the run rate in the remaining 40 overs to reach the target of 282 runs?

a.6.25 b.6.5 c.6.75 d.7

2. A family consists of two grandparents, two parents and three grandchildren.

The average age of the grandparents is 67 years, that of the parents is 35

years and that of the grandchildren is 6 years. What is the average age of the

family?

a.28.6 b.31.6 c.32.7 d.none

3. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5

consecutive months. How much sale must he have in the sixth month so that

he gets an average sale of Rs. 6500?

a.4991 b.5991 c.6001

d.6991

4. The average weight of 8 person's increases by 2.5 kg when a new person

comes in place of one of them weighing 65 kg. What might be the weight of

the new person?

a.76 b.76.5 c.85 d.none

5. The average monthly income of P and Q is Rs. 5050. The average monthly

income of Q and R is Rs. 6250 and the average monthly income of P and R is

Rs. 5200. The monthly income of P is:

a.3500 b.4000 c.4050

d.5000

6. The average age of husband, wife and their child 3 years ago was 27 years and

that of wife and the child 5 years ago was 20 years. The present age of the

husband is:

a.35 b.40 c.50 d.none

7. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three

successive years. What approximately is the average cost per litre of petrol if

he spends Rs. 4000 each year?



a.Rs7.98 b.Rs8 c.Rs8.50 d.Rs9

8. The average weight of A, B and C is 45 kg. If the average weight of A and B be

40 kg and that of B and C be 43 kg, then the weight of B is:

a.17kg b.20kg c.26kg

d.31kg

9. The average weight of 16 boys in a class is 50.25 kg and that of the remaining

8 boys is 45.15 kg. Find the average weights of all the boys in the class.

a.47.55kg b.48kg c.48.55kg d.49.25kg

10. A library has an average of 510 visitors on Sundays and 240 on other days.

The average number of visitors per day in a month of 30 days beginning with

a Sunday is:

a.250 b.276 c.280 d.285

11. If the average marks of three batches of 55, 60 and 45 students is 50, 55, 60,

respectively then the average marks of all the students is:

a.53.33 b.54.68 c.55 d.none

12. A man spends Rs. 750 on an average during first 8 months. During the next 4

months he spends Rs. 680 per month. He took loan of Rs. 320 during the year

and paid Rs. 600 for LIC premium. Find his monthly average income?

a.Rs. 650 b.Rs.750 c.Rs. 850 d.Rs.900

13. Find the least number exactly divisible by 12,15,20,27?

a.380 b.540 c.520 d.440

14. The average age of 24boys & a teacher is 15yrs. When teacher age is excluded,

the average decreases by 1. What is the age of teacher?

a.25 b.30 c.35 d.39

15. The average weight of 29 students is 28kg. By the admission of a new student,

the average weight is reduced to 27.8kg. Find the weight of a new student?

a.22kg b.21.6kg c.35kg

22.4kg

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16. A cricketer has an average score of 24 runs in 24 innings. How many runs

must he score in the 25th innings to make the average 25?

a.24 b.25 c.40 d.49

17. A batsman has a certain average of runs for 25 innings. In the next innings, he scores 156 runs thereby increasing his average by 2 runs. His new average is

a.100 runs b.102 runs c.104 runs d.106 runs

18. Among A, B, C, D, and E, A weighs 2 kg less than B, B weighs 2 kg more than D or E, individually. But C weighs 6 kg more than B. The average weight of these five will be equal to the weight of whom among the following? a.C b.B c.D d.A

19. The average weekly salary per head of the entire staff of a factory consisting of supervisors and the laborers is Rs 60.The average salary per head of the supervisors is Rs 400 and that of the laborers is Rs 56.Given that the number of supervisors is 12.Find the number of laborers in the factory. a.1020 b.1130 c.1010 d.1240

20. Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in

the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third

variety per kg will be:

a. Rs. 169.50 b. Rs. 170 c. Rs. 175.50 d. Rs. 180



















RATIO & PROPORTION

1. 0.75:X = 5:8. Then find x?

A.1.12 B.1.2 C.1.25 D.1.3

2. Divide RS1162 among A,B,C in the ratio of 35:28:20. What is the share of C?

A.300 B.280 C.420 D.none

3. Rs 1210 was divided among A,B,C so that A:B = 5:4 & B:C = 9:10,then C gets

A.340 B.400 C.450 D. 475

4. A mixture contains alcohol & water in the ratio 4:3.If 5l of water is added to the

mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture?

A.8 B.6 C.10 D.7

5. The ratio of incomes A&B is 5:4,and the ratio of their expenditure is 3:2.If at the

end of the year, each saves Rs1600,then income of A is?

A.3400 B.3600 C.4000

D.4400

6. In a mixture of 60l, the ratio of milk & water is 2:1.If this ratio is to be 1:2,then the

quantity of water to be further added is

A.20l B.30l C.40l D.60l

7. A sum of money is to be distributed among A,B,C&D in the ratio 5:2:4:3. If C gets

Rs 1000 more than D, What is B’s share?

A.500 B.1000 C.2200 D.none

8. The average age of three boys is 25yrs & their ages are in the proportion 3:5:7,

the age of the youngest boys is

A.21 B.18 C.15 D. 9



9. A milk man has a mixture of milk in which ratio of milk & water is 4:3.He sells

40litres of mixture, then he adds up 15liters of pure water. Now the ratio of milk &

water is 5:4. What is the new quantity of mixture?

A.675l B.400l C.550l D.350l

10. The ratio of working efficiency of A & B is 5:3 and the ratio of working efficiency

of B & C is 5:8. Who is most efficient?

A.A B.B C.C D.Can,t be determined

11. The students in three classes are in the ratio of 2:3:4. If 50 students are added in

each class, the ratio becomes 4:5:6. Find the total number of students in all the three

classes initially is?

A.250 B.225 C.375 D.250

12. If a carton containing a dozen mirrors is dropped. Which of the following cannot

be the ratio of broken mirrors to unbroken mirrors?

A.3:2 B.3:1 C.2:1 D.7:5

13. The ratio of number of boys to that of girls in a school is 3:2. If 20% boys & 25%

girls are scholarship holders, find the percentage of the school students who are not

scholarship holders.

A.22 B.78 C.72 D.28

14. Sales incentives are distributed to 3 sales man working in the same team. The 3

salesmen are Arun, shree & Sampath. Ratios are 4:1 for both arun’s share to Shree’s

share as well as Shree share to Sampath’s share. Sampath gets Rs 18,000 less than

Arun, find the total incentive

A.RS 25400 B.Rs35200 C.Rs25000 D.none

15. The ratio of A:B = 1:3, B:C = 2:5, C:D = 2:3. Find the value of A&C.

A.12&20 B.4:30 C.30:45 D.4:45

16. The ratio of length to width of a rectangular sheet of paper is 4:3. If the width of

the sheet is 24cm, find its length.

A.32 B.30 C.28 D.35



17. If 121,x,x,169 are in proportion, find x.

A.144 B.143 C.159 D.125

18. If (a+b) : (a-b) = 15:1, then the value of a^3 + b^3 is.

A.163 B.512 C.343 D.144

19. A man bought 9mangoes for a rupee & sold them at 6mangoes for a rupee. What

is the profit ratio to the cost price?

A.3/10 B.3/2 C.1/2 D.none

20. Simplify the ratio 3 ¾ : 4 ½ : 5 2/3.

A.45:18:68 B.20:9:90 C.12:13:16 D.17:13:29



PROBLEMS ON AGES.

1. A mother after 4 yrs will be twice the age of her daughter. The sum of their

ages today is 40. What is daughter’s age today?

2. After 4yrs father’s age will be thrice the age of his son. The sum of their ages

is 56 yrs. Find the father’s age now?

3. Ramya’s age was thrice Sita’s age 5 yrs. If difference of their age now is 16 yrs.

Find the present age of Sita ?

4. Father’s age is 32 yrs more than his son age. After 2 yrs the sum of their ages

is 52. Find the age of the father’s age?

5. The sum of the ages of two brother is ten yrs ago elder brother had twice the

of his younger brothers. What is the age of the elder?

6. The sum of the ages of A & B now is 110 yrs and their ages 20 yrs age where

in the ratio 4:3. Find the age of A?

7. Four years ago the father’s age was three times the age of his son. The total

age of father & son after 4 yrs will be 64 yrs. What is fathers present age.

8. Rohit was 4 times as old as his son 8 yrs ago. After 8 yrs, Rohit will be twice as

old as his son. What are their present ages?

9. One year ago, the ratio of Gaurav and sachin was 6:7. Four yrs hence, the ratio

would become 7:8. How old is sachin?

10. The present age of three persons are in the ratio 4:7:9. Eight yrs ago sum of

their ages was 56. Find their present age?

11. Ten yrs ago Ram was thrice as old as Shyam and 10 yrs hence, he will be only

twice as old as Shyam. What is Ram’s present age?

12. Rajeev’s age after 15 years will be 5 times his age 5 years back. What is the

present age of Rajeev.

13. The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3

times as old as the younger one, find their present ages.



14. The present age of a father is 3 years more than three times the age of his son.

Three years hence, father’s age will be 10 years more than twice the age of

the son. Find the present age of the father.

15. Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be

twice as old as his son. What are their present ages?

16. Abhay’s age after six years will be three – seventh of his father’s age. Ten

years ago, the ratio of their ages was 1:5. What is Abhy’s father’s age at

present?

17. The ratio between the present ages of P and Q is 5:7 respectively. It the

difference between Q’s present age and P’s age after 6 years is 2, what is the

total of P’s and Q’s present ages?

a. 48 years b. 52 years c. 56 years d. can’t be determined e. none of these

18. At present, the ratio between the ages of Arun and Deepak is 4:3. After 6

years, Arun’s age will be 26 years. What is the age of Deepak at present?

a. 12 years b. 15 years c. 19 ½ years d. 21 years

19. Present ages of X and Y are in the ratio of 5:6 respectively. Seven years hence

this ratio will become 6:7 respectively. What is X’s present age in years.

a. 35 b. 49 c. 42 d. can’t be determined e. none

20. Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three

years hence, the ratio of their ages will become 11:9 respectively. What is

Anand’s present age in years?

a. 24 b. 27 c. 40 d. can’t be determined

21. Six year ago, the ratio of the ages of Kunal and Sagar’s was 6:5. Four year

hence, the ratio of their ages will be 11:10. What is Sagar’s age at present?

22. The ratio of the present ages of two brothers is 1:2 and 5 years back, the ratio

was 1: 3. What will be the ratio of their ages after 5 years?

a. 1:4 b. 2:3 c. 3:5 d. 5:6



23. Hitesh is 40 years old and Ronnie is 60 years old. How many years age was

the ratio of their age is 3:5?

a. 5 years b. 10 years c. 20 years d. 37 years

24. The ratio of the father’s age to his son’s age is 7:3. The product of their ages is

756. The ratio of their ages after six years will be :

a.5:2 b.2:1 c. 11:7 d.13:9

25. The ratio between the present ages of A and B is 5:3 respectively. The ratio

between A’s age 4 years ago and B’s age 4 years hence is 1:1. What is the ratio

between A’s age 4 years hence and B’s age 4 years age?

a. 1:3 b. 2:1 c. 3:1 d. 4:1 e. none of these

26. Ten years age, A was half of B in age. If the ratio of their present ages is 3:4,

what will be the total of their present ages?

a. 20 years b. 30 years c. 45 years d. none of these

27. A is two years older than B who is twice as old as C. if the total of the ages of

A,B and C be 27, then how old is B?

a. 7 b. 8 c. 9 d. 10 e. 11

28. A man is 24 years older than his son. In two years his age will be twice the age

of his son. The present age of the son is.


29. Eighteen years ago, a father was three times as old as his son. Now the father

is only twice as old as his son. Then the sum of the present ages of the son and

the father is

a. 54 b. 72 c. 105 d. 108

30. A persons present age is tow fifth of the age of his mother. After 8 years, he

will be one-half of the age of his mother. How old is the mother at present?


31. Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3

times of her age 8 years from the first years ago, what was the ratio of Tanya’s



32. The sum of the present ages of a father and his son is 60 years. Six years ago,

father’s age was 5 times the age of the son. After 6 years, son’s age will be


33. The age of a man is three times the sum of the ages of his two sons. Five years

hence, his age will be double of the sum of the ages of his sons. The father’s

present age is


34. The sum of the ages of a father and his son is 45 years. Five years ago, the

product of their ages was 34. The ages of the son and the father are

respectively.

a. 6 and 39 b. 7 and 38 c. 9 and 36 d. 11 and 34

35. Rajan got married 8 years ago. His present age is 6/5 time his age at the time

of his marriage. Rajan’s Sister was 10 years younger to hims at the time of his

marriage. The age of Rajan’s sister is


36. The sum of the ages of 5 children born at the intervals of 3 years each is 50

years. What is the age of the youngest child?

a. 4 years b. 8 years c. 10 years d. None of these

37. Ayesha’s father was 38 years of age when she was born white her mother was

36 years old when her brother four years younger to her was born. What is

the difference between the ages of her parents?


38. A person was asked to state his age in years. His reply was, ‘Take my age

three years hence, multiply it by 3 and then subtract three times my age three

years ago and you will know how old I am” what was the age of the person?




PARTNERSHIP

SIMPLE PARTNERSHIP

It the capital of the partners are invested for the same period, it is called

simple partnership. The profit or loss is divided as per the investment ration

inv. Of A/Inv of B-Profit of A/Profit of B-Loss of A/loss of B

COMPOUND PARTNERSHIP

It the capitals are invested for different period, it is called compound

partnership. Inv of A* period of inv. Of A* period of A/inv. Of B* period of inv. Of

B=profit of A/profit of B = loss of A/loss of B

WORKING PARTNER

One who works for the company apart from putting the capital, for which he

will get remuneration for managing the business plus the share profit.

SLEEPING PARTNER

A sleeping or idle partner is one who simply in invests the money and share the

profit or loss.

1. A, B and C started a business jointly by investing Rs. 380000, Rs. 400000, Rs.

420000, respectively. What is the profit of C I the annual profit of Rs. 240000

a) 60000 b) 64000 c) 84000 d) 82000 e) none

2. Sundar is a working partner and Vijay is a sleeping partner as a business. Sundar

invests Rs. 5000 and Vijay Rs. 6000 initially. Sundar receives 12.5% of the profit

for managing the business. The remaining amount is divided as per the

investments. What does each get out an annual profit of Rs. 1320.

3. Manoj started a business by investing Rs. 36000 after 3 months vinod joined him

by investing Rs. 36000 out of an annual profit of Rs. 37100, find the share of

Vinod?

4. A, B and C started a business each investing Rs. 20000. After 5 months, A

withdrew Rs. 5000, B withdrew 4000 and C invested Rs. 6000 more. At the end

of the year, the profit was Rs. 69900. Find the share of B?



5. A, B and C invested Rs. 20000, Rs. 30000, Rs. 40000 in a business after 1 year A

removed his money but B and C continued for one more year. It the net profit

after two years was Rs. 32000, Find C’s share in it.

6. A started a business by investing Rs. 45000. After 3 months B joined him with a

capital of Rs. 90000. What is the share of C from the annual profit of Rs. 16500

7. Rajesh began a business with Rs. 2100 and is joined afterwards by Suresh with

Rs. 3600. After how many months did Suresh join it the profit an the end of the

year is divided equally?

8. A, B and C invest Rs 47000 totally in a business. A puts Rs. 7000 more than B

puts Rs. 5000 more then C. out of a total profit of Rs. 94000, find the share of B?

9. Arun, Maya, Shreya Started a business by investing Rs. 27000, Rs. 81000 and Rs.

72000 respectively. At the end of the year the profit was distributed as per their

investments. If Maya’s share of profit be Rs. 36000 the total profit was

10. Two persons P and Q start a business together P invests Rs. 8000. It the shares of

profit of P and Q be Rs. 360 and Rs. 450 respectively, the investment of Q is

a) 9000 b) 12000 c) 10000 d) 15000 e) none



PERCENTAGES

A fraction with denominator 100 is called a percent. Percent is an

abbreviation for the latin word “Percentum” meaning “Per hundred” or “hundredhs”

and is denoted by symbol %

CONVERSION OF A FRACTION IN TO PERCENTAGE

To convert a fraction in to a percentage, multiply the fraction by 100 and put

“%” sign.

1. Convert the following fractions in to percentages.

Conversion of a percentage into a fraction

2. Express the following percentage as fraction

a) 20% b) 30% c) 45% d) 5 1/8% e) 155%

3. Solve the following

a) 38% b) 25% c) 66.66%

4. Convert the following percentage in to decimals

a) 1:5 b) 2:3 c) 4:9

5. Convert the following percentage in to decimals.

a) 36% b) 250% c) 57.5% d) 17 1/5% e) 7%

6. Convert the following decimals into percentages.

7. Find the no of male students (i.e., boys) if there are 42% male students in the

school and the total no. of students in the school is 1000

8. A student scored 85% marks. Total marks were 400. How much did he score?

9. In an orchard 10 2/3 % of the trees are mango trees. It the total number of

trees in the orchard is 360, find the number of other types of trees in the

orchard.

10. What percent is number 3 of number 20?

11. Ravi obtained 325 marks out of a maximum of 400 marks. Find the

percentage of marks obtained by him.



12. In a factory of 150 workers, 18 were absent in a day what percentage were

present.

13. Kurla obtained 480 marks out of 600 and birla obtained 560 marks out of

800. Whose performance is better?

14. The height of abhimanya some times ago was 110cm. Now his height is

120cm. find the percentage change in his height.

15. The total expenses of a hostel were Rs. 8000 per month some students left the

hostel due to which the new expenses come down by Rs. 1000. Find the

percentage decrease in expenses of the hostel.

16. Salary of Raja is Rs. 9000 per month and salary of Rani is Rs. 10000 per

month

i) What per cent is the salary of Rani to that to Raja?

ii) What per cent is the salary of Raja to that of Rani?

17. Salary of Rajeev rattan in 2001 was $100 per day and his salary in 2002 was

$125 per day .again in 2003 his salary was $100 per day.

i) What is the percentage increases in his salary in 2002?

ii) What is the percentage decrease in his salary in 2003 over 2002?

18. Age of Ravi is 20 years. If the Shyam’s age is 25% greater than that of Ravi

then how munch percent Ravi’s age is less than Shyam’s age?

19. Gautam has 33.33% more pencils than Raghul has. By how much percent less

pencils Rahul has than that of Gautam?

20. Height of Amitabh is 50%greater than the height of Amir Khan. Height of

Amir Khan is how much percent less than that of Amitabh?

21. Due to irregular working habits of Ramachandran, his salary was reduced by

20% but after some months his salary was increased to the original salary.

What is the percentage.



22. Kajol usually wears saree, which is 16.66% less than the actual length of the

salree. By how much percent the actual length of the Saree is greater than the

length of saree which Kajol usually wears?

23. The age of B is 50% greater than the age of A. the age of C is 20% less than the

age of B. by how much percentage the age of C is greater than the age of A

24. If the price of a commodity be raised by 20% then by how much percent a

house holder reduce his consumption of the same commodity so that his

expenditure does not increase.

25. If the price of petrol falls down by 20% by how much percent must a person

increase its consumption. So as not to decrease the expenditure on this item?

26. Due to 50% increase in the price of rice. We purchased 5 kg less rice with the

same amount of Rs. 60. What is the new price of rice?

a) Rs. 4.66 b) Rs. 5 c) Rs. 4 d) Rs. 6

27. In an election between two candidates, the candidate who got 57% valid

votes won by a majority of 420 votes find the total no of valid votes.

28. Due to fall in manpower, the production in the factory decreases by 60% by

what percent should the working hour be increased to restore the original

production in the factory?

29. Two numbers are respectively 25% and 40%^ less than a third number what

percent is the second of the first?

30. A person gives 10% to his wife 10% of the remaining to a hospital (as a

donation) again 10% of the remaining to prime ministers relief fund. Then he

has only 7290Rs. With him what was the initial sum of money with that

person?

31. Initially a shop keeper had a chocolates. A customer bought 10% chocolate

form n than another customer bought 20% of the remaining chocolates after

that one more customer purchased 25% of the remaining chocolates. Finally



shopkeeper is left with 270 chocolates in his shop. How many chocolates

were there initially in the shop?

a) 300 b)450 c) 500 d) 600

32. If the annual increase in population be 20% and the present population be

10,000. What will be the population after 3 years hence?

a) 16000 b) 17280 c) 14400 d) 1728

33. The population of a town in the first year increase by 10% in the next year it

decrease by 10% once again in the third year it increases by 10% and in the

fourth it decrease by 10% if the present population be 20,000 then the

population after four years will be.

a) 16902 b) 19602 c) 20000 d) none of these

34. Shwetha is a very expert in bargaing. One she went to a nearby shop. When

shwetha asked the price of shampoo sachet the shop keeper told her the price

by increasing 15% of the original cost. But shwetha insisted to decrease the

price by 15% so the shopkeeper sold it by decreasing the price by 15% what

is the loss or profit of shopkeeper and by how much percent?

a) No loss b) profit of 1.5% c) loss of 2.25% d) none

35. If the length and breadth of a rectangle are changed by +20% and -10% what

is the percentage change in area of rectangle?

a) 8% b) 10.8% c) 20% d) data insufficient

36. The salary of A is 20% lower than B’s salary and the salary of C is 56.25%

greater than A’s salary. By how much percent the salary of B is less than the

salary of C

37. Nithish is now 20 years old. Some years later his age will increase by 50% of

himself. What will be the new age at that time?

38. The average salary of purushottam in Infosys is 20% less than that was in

Microsoft. If the slary of purushottam in Microsoft be $80000 per month then

what is the salary of purushottam in Infosys?



39. Which one of the following is greatest ¾, 7/8. 16/19. 15/15?

40. The price of an item is increased by 20% and then decreased by 20% the final

price as compared to original price.

a) 4% more b) 20% more c) 20% less d) 4% less

41. Two candidates fought an election. One got 65% of the votes and won by 600

votes. The total no of votes polled is

a) 12000 b) 10000 c) 200 0 d) 8000

42. Out of a no of electronic items, a person purchases 60% coloured TVS 5% of

these were found to be defective. The percentage of defective Tvs in all is

a) 3% b) 6% c) 12% d) can’t be determined



PROFIT, LOSS AND DISCOUNT

COSTPRICE (CP) :

The money paid by the shop keeper to the manufacturer or whole saler to buy

the goods is called the cost price (cp) of the goods purchased by the shop keeper.

SELLING PRICE (SP)

The price at which the shopkeeper sells the goods is called the selling price

(sp) of the goods sold by the shop keeper.

PROFIT :

If the selling price of an article is more than its cost price, then the dealer (or)

shopkeeper makes a profit (or) gain.

i.e., Profit = SP-CP; SP> CP

LOSS :

If the selling price of an article is less than its cost price, then the dealer

suffers a loss

1. A fruit seller buys 300 oranges at 5 for Rs. 8 and sold at 2 for Rs. 5 find.

i. The cost price of each orange

ii. The selling price of each orange

iii. Profit or loss on selling one orange

iv. His total profit or loss on selling all the oranges.

2. A shopkeeper buys 100 eggs at Rs. 1.20 per piece. Unfortunately 4 eggs got

spoiled during transportation. The shop keeper sells the remaining eggs at Rs.

15 a dozen. Find his profit or loss.

3. A viral purchased a computer for Rs. 47,000/-. He had to sell it for

Rs. 45,800/-. Find his profit or loss percent.

4. A dealer sold 600 quintals of sugar at a profit of 7% if a quintal of sugar cost

him Rs. 1600. Find his total profit and the selling price.



5. A dealer buys 200 quintals of wheat at Rs. 1200 a quintal. He spends Rs.

10,000 on transportation and storage. There he sells the wheat at Rs. 13 per

kg. Find his profit or loss. Also calculate it as a percentage.

6. Find the cost price of an article which is sold for Rs. 220 at a loss of 12%

7. By selling a color TV for Rs. 23520, a dealer suffers a loss of 4%. What is the

cost price of the color TV? At what price should he sell it to gain 8%?

Discount:

Discount means reduction of marked price to sell at a lower rate or literally

discount means concession. Basically it is calculated on the basis of marked price.

8. If the cost price of an article is Rs. 00 and the per cost markup is 20%. What is

the marked price?

9. If the market price of an article is Rs. 450 and markup percentage is 12.5%.

What is the cost price?

10. If the marked price of an article is Rs. 660 and the discount is 10% then what

is the selling price of the article.

11. If the makeup percentage of an article is 50% an discount percent is also 20%

then the profit percentage will be.

a) 10% b) 0% c) 30% d) 20%

12. A trader markup the goods by 10% and then gives a discount of 10% what is

the profit or loss percentage?

13. Successive discount of 10% and 5% is equivalent to

a) 16.5% b) 15% c) 15.5% d) 14.5

14. A man sells two wrist watches one at a profit of 10% and another at a loss of

10%, but the selling price of each watch is Rs. 200 find the

1. Percentage profit or loss

2. Net amount of profit or loss

15. There were two articles and the sum of cost price of these articles is Rs.500

one of them was sold at a profit of 20% and another at a loss of 20%. Besides



if the selling prices of both the articles were same. Find the amount of overall

loss.

16. If the cost price of 15 apples is same as the selling price of 20 apples. What is

the gain or loss percent?

17. If the selling price of 10 CDs is the same as the cost price of 12 CDs. What is

the profit or loss percent?

18. A dealer by selling 12 oranges gets the cost price of 15 oranges. What is the

percentage profit?

19. By selling 8 bananas, a seller gains the selling price of 1 banana. Calculate his

gain percent.

20. By selling 18 chocolates, a vendor loses the selling price of 2 chocolates. Find

his loss percent.

21. A trader sell all his articles at the cost price but gives 10% less amount as he

should give. What is his percentage profit?

22. A trader by means of his false balance defrauds to the extend of 10% in

buying goods and also defrauds to 10% in selling . find his gain percent.

23. Abhishek and Bhanu both are dealers of KML scooters. The price of a KML

scooter is Rs. 28,000. Abhishek gives a discount of 10% on whole, while

Bhanu gives a discount of 12% on the first Rs. 20,000 and 8% on the rest Rs.

8000. What is the different between their selling prices?

a) Rs. 240 b) Rs. 420 c) Rs. 640 d) none of these

24. A trader sells two articles one at a loss of 10% and another at a profit of 15%

but finally there is no loss or gain. It the total sale price of these two articles is

Rs. 30,000. Find the difference between their cost prices.

a) Rs. 5000 b) Rs. 6000 c) Rs. 7500 d) none of these

25. A milkman purchases the milk at Rs. X per litre and sells it at Rs. 2X per litre

still he mixes 2 litre still be mixes 2 litres water with every 6 litres of pure

milk. What is the profit percentage.



a) 116% b) 166.66% c) 60% d) 100%

26. A retailer bought 20 kg tea at a discount of 10% besides 1 kg tea was treely

offered to him by the wholesales at the purchases of 20 kg tea. Now he sells

all the tea at the marked price to the customer. What is profit percentage of

retailer?

27. Two articles are sold at the same price. One at a profit of 75% and another

one at a loss of 30%. What is the overall profit or loss?

a) 22.5% b) 57.5 profit c) 13 2/7% profit d) none

28. What is percentage profit in selling an article at a discount of 20% which was

earlier being sold at a 40% profit?

a) 20 b) 14 c) 28% d) 12%

29. A man bought 18 oranges for a rupee and sold them at 12 oranges for a rupee.

What is the profit percentage?

a) 33.33% b) 50% c) 66.66% d) none of these

30. A dealer buys a product at Rs. 1920, He sells at a discount of 20% still be gets

the profit of that product?

31. Tinkawala purchased the articles for Rs. 123684. He sold 60% of those at a

profit of 16.66% and rest at a loss. Find the loss percentage on the remaining

it the overall loss is 14%?

a) 20% b) 30% c) 60 % d) 66.66%

32. What should be the minimum markup percentage such that after giving a

discount of 66 2/3% there will not be a loss?

a) 200% b) 133.33% c) 100% d) 150%

33. The ratio of cost price and marked price of an article is 2:3 and ratio of

percentage profit and percentage discount is 3:2. What is discount

percentage?

a) 16.66% b) 20% c) 25% d) 33.33%



34. A dealer gives as much discount (in percent ) as the markup (in percent )

above the cost price. What is the profit or loss percent.

a) 10% b) 1% c) 4% d) cant be determined.

35. Mr. Mittal purchased a car for Rs. 3,00,000 and a bike for his son for Rs.

1,00,000. He sold the car at a profit of 10% and bike at a loss of 20%. What is

the net gain or loss?

a) 2% gain b) 1.5% loss c) 2.5% loss d) 2.5% gain

36. The profit percentage on the three articles A,B and C is 10%, 20% and 25%

and the ratio of the cost price is 1:2:4. Also the ratio of number of articles sold

of A, B and C is 2:5:2 then the overall profit percentage is

a) 18.5% b) 21% c) 75% d) none of these

37. An item was sold after giving two successive discount of 20% and 10%

respectively if . The item was sold for Rs. 468. The marked price of that item is

38. The cost price of an article ‘A’ is Rs. 160 and selling price of another article ‘B’

is Rs. 240. If the selling price of A is 20%. What is the profit on ‘B’?

a) 16.66% b) 50% c) 25% d) none

39. A single discount equivalent to three successive discounts of 5%, 10% 20% is

a) 68.4% b) 35% c) 31.6% d) 32%

40. Ragini purchases oranges at Rs. 10 per dozen and sells them at Rs. 12 for

every 10 oranges. What is the profit percentage?

a) 40% b) 44% c) 60% d) 48%

41. A trader uses a weighing balance that shows 1250 g for a kilogram. He further

marks-up his cost price by 20%. What is the profit percentage?

a) 5% b) 45% c) 50% d) 30%

42. On selling an article for Rs. 240, a trader loses 4%. In order to gain 10% he

must sell that article for

a) Rs. 275 b) Rs. 340 c) Rs. 320 d) Rs. 264.



43. A merchant marks his goods at Rs. 300 and allows a discount of 25%. If he

still gains 125% then the cost price of article is

a) Rs. 220 b) Rs. 200 c) Rs. 240 d) Rs.260

44. An item costing Rs. 200 is being sold at 10% loss. If the price is further

reduces by 5% the selling price will be:

a) Rs. 170 b) Rs. 171 c) Rs. 180 d) Rs. 181

45. A person sold two cows each for Rs. 9900. If he gained 10% on one and lost

20%. On the other, then which of the following is true?

a) He gained Rs. 200 b) He lost Rs. 200

b) He neither gained or loss d) None of the above

46. Two third of a consignment was sold at a profit of 5% and the remainder at a

loss of 2%. If the total profit was Rs. 400, the value of the consignment (in

rupees) was:

a) 15000 b) 20000 c) 10000 d) 12000

47. A fruit seller declares that he sells fruit at the cost price. However, he uses a

weigh of 450g instead of 500g .His percentage profit is:

a) 10% b) 11 1/9% c) 12% d) 12 2/9%

48. Due to an increase of 30% in the price of eggs , 3 eggs less are available for Rs.

9.10. The present rate per egg is

a) 91 paise b) 78 paise c) 48 paise d) 84 paise

49. By selling 12 apples for a rupee, a man loses 20%. How many for a rupee

should he sell to gain 20%?

a) 8 b) 10 c) 15 d) 16.

50. A dealer buys a washing machine, listed at Rs.10000 and gets 10% and 20%

successive discount. He spends 10% of his cp on transport. At what price (in

rupees) should he sell the washing machine to earn a profit of 10%?

a) 8722 b) 7892 c) 8712 d) 8840



TIME AND WORK

1. A can do work in 10 days and b can do in 15 days. If both combined how

many days it will take.

2. A → 30 days B → 40 days A+B→? days

3. A → 10 days B → 20 C → 60 days A+B+C? days

4. P → 15 days ; Q → 60 days R → 80 days, P+Q+R=? days

5. A and B → 15 days; B and C → 20 days; C and → 60 days find the time taken

for working together

6. A and B → 14 days, A alone in 21 days. Find the time taken by B alone.

7. 10 men can do in 80 days, what is the time taken by 40 men

8. 30 men →7hr/day → 18 days

21 men → 8hr/day→? Days

9. 3 men → 3 job in 3 days

100 men → 100 job in? Days

10. 52 monkeys → 52 bananas → 52 minutes

19 monkeys → 19 bananas → ? minutes

11. m men → m day →m hours → m unit

n men → n day → n hours → ? unit

12. 60 examiner → correct 600 papers → 5 days → 8 hours

80 examiner → correct 400 papers → 4 days → ? hours

13. 6 men or 8 women → 42 days

9 men and 12 women → ? days

14. 3M or 6 W or 9b → 20 days

2M+6W+3b→? days

15. 2 M or 2 W or 6 boys → 24 days

1 M + 1 M + 1 boy →? days



16. A → 30 days B → 40 days. Together get a payment of Rs.7000 and find shares

of each.

17. A → 6 days. B → 8 days with the help of C they finished work in 3 days & find

shares of each in 4000

18. A → 12 days

V → 15 days Rs. 10800

A+B+C→ 5 days

19. A → 30 days, B → 40 days with help of C how many days A+B+C→? find daily

earnings of A is Rs. 3000

20. A+B= 7/11 of total work. Find the share of C in Rs. 2200

21. A → 4 days; B→12 days. They work on alternate days with A starting a job.

What is the time taken.

22. A → 9 days; B→12 days with A starting a job. What is time taken.

23. A →15 days; B → 12 days. Alternate days A starting find the time taken.

24. A→30 days; B →50 days. Alternating B staring. Find time taken

25. A →12 days; B→15 days; C → 25days. Alternate in order of B C A

26. A→20 days B → 30 days. A starts the work and worked for 6 days. Then B

completed the remaining part of work. In how many days the work completed

in all.

27. A can 24 days, B→48 days. B joins A after had worked alone for 6 days. In

how many more days would the work be completed.

28. A, B, C can do a job in 9,13 and 36 days. A starts the work and B join A after

one day, C joins them after 3 more days. In how many more days the work

completed.

29. A can do in 10 days & B→12 days. A start the work and after 6 days B also

joined. In how many days total work is completed.

30. A →9 days, B → 10 days C → 15days B and C starts the work and forced to

leave after 2 days. Find the time taken by A to complete work.



31. A → 24 days , B is 50%more efficient than A. Find the time taken by B.

32. A is 20% more efficient than B. A and B together it take 60 days to do a job.

Find time taken by B alone.

33. P is half as fast as Q and thrice as fast as R. If R all the 3 can do job in 30 days.

Find the time taken by P alone.

34. A is twice as good a workman as B. Takes 10 days less to do job than B takes.

Find the taken by B alone.

35. A efficient 3 times of B and takes 60 days less than B. Find the time taken by A

and B.

36. 8M→ 16 days; after 4 days 4 men joined them. The remaining work finished

in how many days.

37. A certain number of men can do a work in 35 days. If 10 men more they do in

25 days. How many men there were initially.

38. 120 M has provigen for 200 days. After 5 days 30 M died. The remaining food

will asked how many days.

39. In a Fort Ration for 2000 people sufficient for 54 days. After 15 days more

people Came & Ration lasted only for 20 more days. How many people came.

40. A and B take 80 days and 20 days respectively more than the time taken by A

and b together. Find the time taken by A & B together.

41. If 2M or 3W can do job in 12 days. How many should a company 6W to

complete the work in 4 days.

42. 1M and 3B can complete ajob in 10 days. 1W alone in 20 days. How many

women should accompany 3M and 9 Boys? Show that the work is complete in

2 days.



SIMPLE INTEREST AND COMPOUND INTEREST

SI = PTR/100

P = Principle

T = Time in years

R = Rate of interest

1. Sudha borrowed Rs.400 from a friend at the rate of 12% per annum for 2

years 6 months. What is the interest and the amount paid by her

a) 140,540 b) 130,530 c) 125,525 d) 120,520 e) none

2. Find the rate percent per annum at which the interest on Rs. 550 is Rs. 66 in 3

years?

a) 3% b) 4% c) 5% d) 6% e) none

3. In how many years will a sum of Rs.3000 gives an interest of Rs. 1080 at 12%

per annum?

a) 3 b) 4 c) 10 d) 5 e) none

4. A shopkeeper borrowed Rs. 25000 from two money lenders. For one loan be

paid 12% per annum and for another 14% per annum. The total interest paid

for one year was Rs. 3250. How much did he borrow from each person?

a) 25000 b) 5000 c) 12500 d)2500 c) none

5. In how many years, an amount invested in a bank gets doubted at 10% rate

of interest

a) 10 b) 15 c) 20 d) 12 e) none

6. In how many years an amount invested in a bank becomes four times at 15%

rate of interest?

a) 10 b) 20 c) 21 d) 15 c) none

7. The SI on a sum of money is 1/9 th of the principal and the no. of years is

equal to the rate of interest. Find the rate of interest?

a) 1 1/3 % b) 21/3 % c) 31/3 % d) 41/3 % e) none



8. A sum of Rs. 425 on SI amounts to Rs. 476 in 3 years. Find the rate of interest.

Find the rate of interest?

a) 2% b) 3% c) 5 d)4 e) none

9. Some amount out of Rs. 5000 was lent at 5% per annum and the remaining

amount at 4% epr annum. If the total simple interest from both in 5 years was

rs.1100, calculate the sum lent at 5%?

a) 1500 b) 10000 c) 2000 d)2800 e) none

10. Find the rate at which a sum becomes four times itself in 15 years at simple

interest?

a) 15% b) 17½ % c) 20 d) 23 e) none

11. An amount gets doubled in 3 years in SI. When this amount becomes 8 times

of itself?

a) 1 b) 10 c9 d)21 e) none

12. A sum of Rs. 12500 amounts to Rs. 15500 in 4 years at the rate of SI. What is

the rate of interest?

a) 3% b) 4 c) 5 d)21 e) none

13. What is the present worth of Rs. 132 due in 2 years at 5% SI?

a) 112 b) 118.80 c) 120 d)122 e) none



COMPOUND INTEREST.

In this, if interest is not paid on the principal, then the interest will be added

to the principal and for the next period the interest will be calculated on the

new principal and so on.

P = Principle

T = Time in years

R = Rate of interest

A = Amount

Amount= P+I

a) When CI compounded annually: A = P(1+ r / 100 )^n.

b) When CI compounded half yearly: A = P(1+ r / 200)^2n.

c) When CI compounded quarterly: A = P(1 + r / 400)^4n.

1. Calculate the CI on a sum of Rs. 800 at 5% rate in 2years?

a) 52 b)62 c)882 d)82 e)none.

2. Calculate the CI on Rs.6250 at 14% per annum for 2years compounded

annually?

a) 872.50 b)1875.50 c)8122.50 d)187.50 e)none

3. Find the difference b/w CI & SI on a sum of Rs.5000 at 10% rate for 1 year?

a) Rs.50 b) Rs100 c)500 d)no diff e)none

4. Find the difference b/w CI & SI on a sum of Rs.5000 at 10% rate for 2 year?

a)no diff b)100 c)50 d)1000 e)none

5. The difference b/w CI & SI on a certain sum of money at 10% per annum for 2

years is Rs.40. find the sum.

a) 5000 b)50000 c)40000 d)4000 e)none

6. The difference b/w CI & SI on a certain sum for 2 years at 5% per annum is

Rs.15. find the sum.

a) 5000 b)6000 c)7250 d)7000 e)none



7. If the amount of Rs.2000 after 3 years becomes Rs.2662. Find the rate of

compound interest?

a)15% b) 6% c)10% d)12% e)5%

8. The difference between CI & SI an a certain sum at 10% per annum for 2

years is Rs.631. find the sum?

a) 65000 b) 55800 c) 54200 d) 62700 e) 63100

9. If the CI of a certain sum for 2 years at 5% be Rs.328, then what will be the

SI for the same sum, rate and time?

a) 300 b) 3000 c) 320 d) 130 e) none

10. A sum amounts to Rs. 1352 in 2 years at 4% compound interest. The sum

is.

a)1250 b) 1420 c) 1190 d) 1120 e) none



THE SPEED DISTANCE & TRAINS.

When a body moves from a point A to another point B at a distance of D, then

it requires some time (T) to cover a distance (D) with a particular speed (S) The relation between T.S and D is as follows: T x S=D Time x Speed =Distance. SPEED Speed of an object is the distance covered by it in a unit time. Speed = Distance Time UNIT OF SPEED

1. If distance is measured in kilometer and time is measured in hours then the unit of speed is kilometer per hour (km/hr)

2. If distance is measured in metre and time is measured in second, then the unit of speed is metre per second (m/sec)

Conversation of kilometre / hour into metre / second 1km = 1000m 1hour = 3600sec 1km/1hr = 1000/3600 m/sec 1 km/hr = 5/18 m/sec Conversation of metre/second in to kilometer/hour 1m = 1/1000 km And 1sec = 1/3600 hr 1m/sec = 3600/1000 km/hr 1m/sec = 18/5 km/hr AVERAGE SPEED Average speed of an object is defined as the ratio of total distance covered to the total time taken Some useful relations:

1. Speed = distance / time 2. Distance = speed x time 3. Time = distance / speed 4. Average speed = Total distance covered / Total time taken



1. Abhishek drives his like at the speed of 150 km/h what is the distance

covered by him in 3 hours

2. Udai travels half of his journey by train at the speed of 120 km/h and rest half by car at 80 km/h. What is the average speed?

3. Speed of Karan is 40 km/h and speed of Arujun is 60 km/h what is the ratio of time taken by each to cover the same.

4. A car half of the time taken by truck to go from Lucknow .

5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train in 54 km/hr, find the length of the platform?

6. A train running at 48 km/hr crosses a telegraph post in 15 seconds. Find the time it will take to cross a bridge 240m long?

7. Two trains moving in the same direction at 65km/hr and 45km/hr. the faster train crosses the man in slower train in 18 seconds. Find the length of the faster train?

8. A train crosses a platform 100m long in 60 seconds at a speed of 45km/hr. the time taken by the train to cross an electric pole is a) 8 sec b) 52 sec c) 1 min d) 44 sec

9. A train 150m long is running at the speed of 90 km/hr. Time taken by the

train to pass through a tree is a) 3 sec b) 4 sec c) 6 sec d) 8 sec

10. A train passes over a bridge of length 200m in 40 seconds. If the speed of the

train is 81 km per hour, its length is A) 900m b) 1800m c) 700m d) 600m

11. A train 150m long takes 20 seconds to cross a platform 50 meter long. The

speed of train is



a) 36km/hr b) 42km/hr c)76km/hr d)108km/hr

12. 150 meters long train crosses a bridge of length 250 meters in 30 seconds. The time for train to cross a platform of 130 meters is a) 18 sec b) 21 sec c) 24 sec d) 27 sec

13. A train 100 meters long is running at the speed of 65 km/hr. Time taken by

the train to pass through a man walking at the rate of 5 km/hr moving in opposite direction is . a) 10 sec b) 8 sec c) 6 sec d) 4 sec

14. A train 100 meters long is running at the rate of 55km/hr. Time taken by the train to pass through a man walking at the rate of 5 km/hr moving in opposite direction is

a) 10 sec b) 8 sec c) 6 sec d) 4 sec

15. A train travelling at a speed of 90 km/hr, crosses a pole in 10 seconds. The length of the train is a) 250m b) 150m c) 190m d) 100m

16. A train takes 18 seconds to pass completely through a station 162m long and 15 seconds through another station 120 m long. The length of the train is a) 250m b) 150m c) 190m d) 100m

17. A train passes a 50m long platform in 14 seconds and a man standing on the platform in 10 seconds. The speed of train is a) 24km/hr b) 36km/hr c) 40km/hr d) 45km/hr

18. An express train travelling at 80km/hr overtake a goods trains, twice as long

and going at 40km/hr on a parallel track in 54 seconds. How long will the express train to cross a station 400m long? a) 36sec b) 45sec c) 27sec d) 32sec.



19. Two trains of long 150m and 120m are travelling at the rate of 75 km/hr and 45 km/hr respectively. Time taken by the trains to cross each other if they travel in the same direction is a) 25sec b) 28.4sec c) 8.1sec d) 32.4sec

20. Two trains of length 150m and 120m are travelling at the rate of 75km/hr

and 45km/hr respectively. Time taken by the trains to cross each other if they travel in opposite direction is a) 5sec b) 8.1sec c) 28.4sec d) 32.4sec

21. Local trains leave from a station at on interval of 15 minutes at a speed of 16

km/hr. A man moving from opposite side meets the train at an interval of 12 minutes. The speed of the man is A) 4km/hr b) 6km/hr c) 8km/hr d) 10km/hr

22. A train running at a speed of 52 km/hr takes 15 seconds to pass a man

running at 4km/hr in the same direction. The length of the train is a) 100m b) 150m c) 200m d)250m

23. Two trains travel in opposite direction at 36 km/hr and 45km/hr and a man

sitting in slower train passes the faster train in 8 seconds. The length of the faster train is a) 80m b) 100m c) 120m d) 180m

24. A train travelling with a constant speed crosses a 96m long platform in 12

seconds and another 14/m long platform in 15 seconds. The length of the train is a) 80m b) 64m c) 84m d) 90m

25. A train passes by a stationary man standing on the platform in 7 seconds and passes by the platform completely in 28 seconds. If the length of the platform in 330 metres, the length of the train is a) 130m b) 125m c) 120m d) 110m



26. A train is running at 120km/hr and is 250m long. How long will it take to pass a goods train 350m long and running on a parallel track at 30km/hr in the same direction? a) 24sec b) 26sec c) 20sec d) 18sec

27. A train passes a station platform in 36 seconds and a man standing on the

platform in 20 seconds. If the speed of the train in 54km/hour, What is the length of the platform? a) 120m b) 240m c) 340m d) 300m e) none of there

28. Two train 100m and 120m long are running in the same direction with

speeds of 72km/hours and 54 km/hours. In how much time will the first train cross the seconds one? a) 40 sec b) 44sec c) 46sec d) 50sec

29. A train 240m long passed a pole in 24 seconds. How long will it take to pass a

platform 650m long? a) 65sec b) 89sec c)100sec d) 150sec

30. How long does a train 110m long running at the speed of 72km/hour take to

cross a bridge 132m in length? a) 9.8 sec b) 12.1 sec c) 12.42 sec d) 14.3 sec

31. A 260m long train crosses a 120m long wall in 19 seconds what is the speed

of the train? a) 27km/hr b) 49km/hr c) 72km/hr d) 70km/hr

32. A 270m long train running at the speed of 120 km/hr crosses another train

running in opposite direction at the speed of 80km/hr in 9 seconds. What is the length of the other train. a) 240m b) 320m c) 260m d) 230m e) none

33. A train covers a distance of 12km in 10 minutes . If it takes 6 seconds to pass a

telegraph post, then the length of the train is



a) 90m b) 100m c) 120m d) 140m

34. How many seconds will a 500m long train take to cross a man walking with a speed of 3 km/hour in the direction of the moving train, if 3km/hour in the direction of the moving train , if the speed of the train is 63km/hour a) 25 b) 30 c) 40 d) 45

35. Two goods train each 500m long are running in opposite direction on parallel

tracks. Their speeds are 45km/hours and 30km respectively. Find the time taken by the slower train to pass the driver of the faster one a) 12sec b) 24sec c) 48 sec d) 60 sec

36. The length of the bridge, which a train 130m long and travelling at 45km/hr

can cross in 30 seconds a) 200m b) 225m c) 245m d) 250m

37. A train running at a speed of 120 km per hour crosses a signal post in 15

seconds. What is the length of the train in metres? a) 300 b)200 c) 500 d) Can’t be determined e) none

38. A 300m long train crosses a platform in 39 seconds while it crosses a signal

pole in 18 seconds. What is the length of the platform? a) 320m b) 650m c) 350m d) data inadequate e) none

39. A train when moves at an average speed of 40km/h reaches its destination on

time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes late. Find the length of journey? a) 30km b) 40km c) 70km d) 80km



BOATS AND STREAMS

a) If the speed of water in any river or stream is zero, them it is called still water b) If the water in the river is moving in any direction, then it is called running

water or stream water. c) If the water is moving along the direction of stream, then it is called down

stream. d) If the water is moving against the direction of stream, then it is called

upstream. e) Let the speed of boat (swimmer) in still water be x km/hr and the speed of

stream is y km/hr, then the boat’s (swimmers) Speed in downstream = (x+y) km/hr Speed in upstream = (x-y) km/hr

f) If the speed of boat (swimmer) in downstream is ‘a’ km/hr and speed of boat (swimmer) in upstream is ‘b’ km/hr then, the boat (swimmers)

Speed in still water = a+b/2 km/hr Speed of stream warer = a-b/2 km/hr

g) When the downstream distance is equal to the upstream distance then the time taken by the boat (swimmer) to cover the whole journey is given by boat’s (swimmer’s) speed in still water x total distance/ speed in downstream x speed in upstream.

h) When the downstream distance is equal to the upstream distance then the time taken by the boat (swimmer) to cover the whole journey is given by. Boat’s (swimmer’s) speed in still water x total distance/ speed ion downstream x speed in upstream.

1. A person can row down a stream at 6km per hour and up the same stream at 3 km per hour and up the same stream at 3 km per hour. Find his rate in still water.

2. A man can row at the rate of 9 km per hr in still water. At what rate can be row against a stream flowing 7 km per hour?

3. A man rows 15km downstream in 3hours 45minutes and 5 km upstream in 2

hours 30 minutes. Find his speed in still water and also the speed of the current.

4. A man row at a speed of 9km/hr in still water and back to the place n the

river which flows at 3 km/hr. Find his average speed of the total journey.



5. A man can row 30km upstream and 44km downstream in 10hours. Also he can row 40km upstream and 55km downstream in 13 hours. Determine his speed in still water and speed of the stream.

6. A man can row 6km/hr in still water and he finds that it takes twice as long in rowing up as in rowing down the river. Find the rate of the current.

7. 1 & the downstream rate of a boat is 12km/hr and upstream rate is 9km/hr.

Also it takes 4 hours 12minutes in going from P to Q and from Q to P back. Find the distance between P and Q.

8. A person can row down a stream at 6 km/hr and up the same stream at 3km

per hour. The rate of flow of stream is

a) 1.5 km/hr b)2.5km/hr c)4.5km/hr d)9km/hr.

9. A person can row at the rate of x km/hr upstream and at the rate of y km/hr downstream. The rate in still water is a) X + y b) x –y c) x – y/2 d) x + y/2

10. A person rows 1 km downstream in 10 minutes and 1km upstream in

30minutes. The velocity of current is a) 1km/hr b) 2km/hr c) 4km/hr d) 1.5km/hr

11. A boat goes downstream at 6 km/hr and upstream at 2km/hr. The speed of

boat in still water is a) 2km/hr b) 205km/hr c) 3km/hr d) 4km/hr

12. A boat takes thrice as much time to sail in the upstream of a river as it would

have taken to sail in the downstream. If the speed of the water is 5km/hr then the speed of boat in still water is a) 4km/hr b) 6km/hr c) 10km/hr d) 8km/hr

13. A boat is rowed down a river at the speed of 1km in 6 minute and up the

river at the speed of 6 km per hour. The speed of current of water is. a) 2km/hr b) 205km/hr c) 3km/hr d) 4km/hr



14. If rows 15km upstream and 21km downstream taking 3 hour each time, then the speed of current is a) 1km/hr b) 1.5 km/hr c) 2km/hr d) 12km/hr

15. A streamer is going at a speed of 4.5 km/hr in still water to a certain

upstream point and back to the starting point in a river which flows at 1.5 km/hr. The average speed of the streamer for the total journey a) 12km/hr b) 9km/hr c) 6km/hr d) 4km/hr

16. A man rows 750 m in 675 seconds against the stream and returns in 450

seconds. This rowing speed in still water a) 3km/hr b) 4km/hr c) 5km/hr d) 6km/hr

17. A person can swim in still water at 4 km/hr. If the speed of water is 2km/hr,

how many hours will the man take to swim back against the current for 6km? a) 2hrs b) 3hrs c) 4hrs d) 5hrs

18. A man can row 9 1/3 km/hr in still water and finds that it takes time thrice as

much time to row up than as to row down the same distance In the river. The speed of the current is a) 3 1/3 km/hr b) 3 1/9 km/hr c)4 2/3 km/hr d) 14km/hr

19. The speed of a boat in still water is 15km\hr and the rate of current is

3km/hr. The distance travelled downstream in 12 minutes is a) 3.6 km b) 2.4km c) 1.2km d) 1.8km

20. A boat is rowed down a river at 16 km per hour and up the river at 8 km per

hour then the velocity of the river is a) 4km/hr b) 8km/hr c) 12km/hr d) 16km/hr

21. A boat goes 40km upstream in 8 hours and a distance of 36km downstream in

6 hours. The speed of boat in standing water is a) 5km/hr b) 5.5km/hr c) 6km/hr d) 6.5km/hr



22. Speed of a boat in still water is 9km/hr and the speed of the stream is 1.5km/hr. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is a) 16 hours b) 18 hours c) 20 hours d) 24 hours

23. A man can row a boat at 10 km/hr in standing water. If the speed if the

stream is 6km/hr, the time taken to row a distance of 80km down the stream is a) 8 hours b) 5 hours c) 10 hours d) 20 hours

24. A boat takes 4 hours for travelling downstream from point A to point B and

coming back to point A upstream. If the velocity of the stream is 2km/hr and the speed of the boat in still water is 4km/hr. The distance between A and B is a) 4km b) 6km c) 8km d) 9km



PERMUTATION AND COMBINATION

Permutation – Arrangements

Combination – selections

If it is permutation then,

npr=n!/(n-r)! =6p2 = 6!/4! =6*5*4!/4! =30

If it is combination then,

ncr =n!/(n-r)!r!;

11c4= 11!/(11-4)! *4! =11*10*9*8*7!/7!*4*3*2*1 =330

1. Evaluate =40!/38!

2. How many words can be formed by using all letters of the word BIHAR?

3. How many words can be formed by using word DAUGHTER so that the

vowels always come together?

4. How many words can be formed from the letter of the word ‘EXTRA’, so that

the vowels are never together?

5. How many words can be formed from the letter of the APPLE?

6. How many words can be formed from the letter of the LEDER?

7. How many words can be formed by using the MANAGEMENT?

8. In how many ways 4 digit numbers can be formed with the digits 3, 5, 7 and 9

only?

9. How many 3 digit number can be formed where unit digit is always zero and

repetition of digit is not allowed?

10. How many four digit numbers can be formed with the digits 0, 2, 3, 5, 8, 9, if

i) repetition of digit is allowed? Ii) repetition of digit is not allowed?



11. In how many ways can a cricket eleven be chosen out of a batch of 15 players?

12. In how many ways a committee of 5 members can be selected from 6 men & 5

ladies consisting of 3 men and 2 ladies?

13. In an examination a candidate is request to answer 6 out of 10 question which

are divided in to two group , each containing 5 question and he is not

permitted to attempt more than 4 questions from each group in how many

ways can he make up his choice?

14. A box contains two white balls, 3 black balls , and 4 red balls . In how many

ways can 3 balls be drawn from the box if at least one black ball is to be

included in the draw?

15. Out of 3 books on economics 4 books of political science and 5 books on

geography how many collections can be made if each collection consists of

exactly one book on each subject?

16. There are 6 boys and 3 girls in a class, a committee of 5 is to be selected such

that 3 boys and 2 girls are on the committee?

17. In how many ways can lawn tennis mixed doubles be made up from 7

married couples if no husband and wife play in same set?

18. A committee of 6 is to be formed from 6 boys and 4 girls in how many ways

can this be done if the committee contains? i) 2 girls ii) at least 2 girls

19. A box containing 2 white balls, 3 black balls and 4 red balls. In how many

ways can 3 balls be drawn from the box, if at least one black ball is to be

included in the drawn?

A)32 b)48 c)52 d)64 e)none

20. Letters of the word DIRECTOR are arranged in such a way that all the vowels

come together find out the total number of ways for making such

arrangement?

A) 4320 b) 2720 c) 2160 d) 1120 e) none.



21. How many letters arrangement can be made from the letters of the word

recover?

A) 1260 b) 1340 c) 12230 d) 15570.

22. There are 11 members in a family out of which there are 4 males and

remaining female. The family has hired three cars for a trip to 300 the

members are to be seated in cars in such a way that the are not more than 4

members in one and there is at least one male in each car. how many

different ways can the members travel?

A) 458 b) 126 c) 140 d) 532 e) none.

23. In how many different ways can the letters of the word DETAIL be arranged

in such a way that the vowels occupy only the odd positions?

A)120 b)60 c)48 d)32 e)none

24. The number of ways in which 6 men and 5 women can dine at a round table if

no two women are to sit together is given by

A)6!*5! B) 5!*4! C) 30 d) 7!*5! E)none

25. The number of ways in which a committee of 3 ladies and 4 gentleman can be

appointed from a meeting consisting of 8 ladies and 7 gentleman if mrs x

refuse to serve in a committee if mrs y is it member is

a)1960 b)3240 c)1540 d)none

26. In how many different ways can the letters of the word ‘PADDLED’ be

arranged

a)901 b)2520 c)5040 d)840

27. A student is to answer 10 out of 13 questions in an exam such that he must

choose at least 4 from the first questions the number of choices available to

him is

a)140 b)280 c)196 d)346

28. The number of ways in which four letters of the word MATHEMATICS can be

arranged is

a) 136 b) 2425 c) 680 d) 346.



PROBABILITY

Probability – possibilities If we toss a coin, there are two possible outcomes, Viz, head (H) and tail (T). So the sample space in this random experiment is S = (H,T) If two coins are tossed 2 coin S = (HH, HT, TH, TT) 2 = 4 (sample)

3 coin 3 = 9 (sample)

S – { (HHH), HHT, HTT, TTT, THH, TTH, THT, HTH}

If we throw a un biased a Die

It gives b possible out comes viz.,

1,2,3,4,5 and 6. So the sample space

s = { 1,2,3,4,5,6}

When two unbiased Dice are thrown (or) rolled wil get 6x6 = 36 possible outcomes.

When three dice are thrown we will get 6x6x6=>63

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) ……………………………….(3,6)

s= (4,1) ……………………………….(4,6)

(5,1) ………………………….(5,6)

(6,1) ………………………….(6,6)

When the die and a win are tossed s ={h1,2h,3h,4h,5h,6h,1t,2t,3t,4t,5t,6t} totally 12 outcomes.

1. In a throw of a coin find the probability of getting a head?

2. Two unbiased coin are tossed what is the probability of getting at least most one

head?

3. An unbiased die is tossed find the probability of getting multiple of 3?

4. In a simultaneous throw of a pair of dice, find a probability of getting total more

than 7?



5. A bag contains 6 white and 4 black balls, 2 balls are drawn at random find the

probability that they are of the same colour?

6. Three coins are tossed simultaneously find the probability of getting one head?

7. Three coins are tossed simultaneously find the probability of getting at least one

head?

8. Three coins are tossed simultaneously find the probability of getting at least two

head?

9. Three coins are tossed simultaneously find the probability of getting at least one

head and one tail?

10. An unbiased die is rolled find the probability of getting a number less than 7 but

greater than zero?

11. An unbiased die is rolled find the probability of getting a prime number?

12. An unbiased die is rolled find the probability of getting multiple of 3?

13. An unbiased die is rolled find the probability of getting an even number?

14. Two dice are rolled simultaneously find the probability of getting total nine?

15. Two dice are rolled simultaneously find the probability of getting more than 9?

16. Two dice are rolled simultaneously find the probability of getting the sum of

numbers on the two faces divisible by 3(or)4?

17. Two dice are rolled simultaneously find the probability of getting a sum as

prime numbers?

18. Four dice are rolled out find the probability of all of them show the same face?



One card is drawn from a pack of 52 cards each of the 52 cards being equally

likely to be drawn find the probability of (19 to 22).

19. The card is drawn black?

20. The card drawn is a queen?

21. The card drawn either king or a queen?

22. Neither a spade nor a king?

23. A bag contains 8 red and 4 green balls. Find the probability that all the 4 balls

drawn are red when four balls are drawn at random?

24. A bag contains 8 red and 4 green balls. Find the probability that three balls are

drawn and none of them is red?

25. A box contains 5 defective and 15 non defective balls two bulbs are drawn at

random find the probability that both the bulbs are non defective?

26. A box contains 6 red balls, 7 green balls, and 5 blue balls each ball is of a

different size. The probability that red ball selected is the smallest red ball is

a)1/18 b)1/3 c)1/6 d)2/3.

27. In a box carrying one dozen of oranges, one third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one orange out of three oranges picked up is good? a)1/55 b)54/55 c)45/55 d)3/55.

28. A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other narrating the same incidents?

a) 5% b) 15% c) 25% d) 35%

29. If four marbles are drawn at random, what is the probability that two are red and two are blue



a) 6/1001 b) 1/143 c) 1/13 d) 6/91

30.If two marbles are drawn at randown, what is the probability that they are green?

a) 4/91 b) 51/91 c) 4/13 d) 1/13 e) none

31. If there marbles are drawn at random, what is the probability that at least one is red

a) 6/13 b) 3/91 c)1/91 d) 3/13

32. If three marbles are drawn at random, what is the probability that none of than are black?

a) 6/13 b) 3/91 c) 5/91 d) 3/13

33. Three dice are thrown simultaneously. What is the probability to obtain only the odd number?

a) 1/12 b) 1/6 c)1/8 d) ¼

34. The probability that a certain electronic component fails when first used is 0.10. If it does not fail immediately then the probability that it will last for one year is 0.99. The probability, that a new component will last for one year is

a) 0.891 b) 0.92 c) 0.692 d) none

35. Out of 13 applicant for a job there are 5 woman and 8 men. It is desired select 2 person for a job. The probability that atleast one of the selected person will be woman is

a) 25/39 b) 5/13 c) 14/39 d) 10/13



CALENDERS

INTRODUCTION Calenders have been used since ancient time for finding the days of the week on a particular given date. The Indian calenders are known as SAKA CALENDERS still used in complex astronomical calculations. Now a days the most accepted calenders are JULIAN CALENDER’S or ROMAN CALENDERS. ODD DAYS Number of days more than the complete number of weeks in a given period is the number of odd days during that period. They can be calculated by dividing the total number of given days by 7. The remainder left is number of odd days. ORDINARY YEAR A year which has 365 days is called as ordinary year. LEAP YEAR A year which has 366 days is called leap year. A leap year is always divisible by 4. 1984, 1992, 1996, 2004 etc. is a leap year. SOME IMPORTANT POINTS

1. Number of odd days play an important role in finding the particular day of a particular year

2. Every 4th century is a leap year but no other century is a leap year. E.g. 400,800,1200,2000 etc. is a leap year but 1100, 2100,2700,1900 etc. is not a leap year.

3. For making calculations easy the number of days in a year is given by Months No of days in

ordinary year No. of days in leap year

Jan 1 to March 31 90 91 Apr 1 to June 30 91 91 July 1 to sep 30 92 92 Oct 1 to Dec 31 92 92 Jan 1 to Dec 31 365 366

4 In a leap year February has 29 Days otherwise in ordinary year it has 28 Days. 5 Odd days can be counted as follows:

a) 1 Ordinary year=365days=(52 Weeks+1day) (1 Week=7 days)



An Ordinary year has 1 odd day b) 1 leap year =366 days =(52 weeks+2day)

A leap year has 2 odd days. c) 100 years have 5 odd days.

100 years=76 Ordinary year + 24 leap year = [(76*52) week +76 days]+[24*52 week+48 days] =3952 weeks + 76 days+1248 weeks + 48days =5200 weeks + 124 days =5200 weeks + (119+5) days =5200 weeks + (17 weeks +_ 5 days =5217 weeks + 5 days 100 years has 5 odd days. Similarly 200 years has 3 odd days 300 years has 1 odd days and 400,800,1200,1600 etc has a 0 odd day.

1. A boy was born on April 6 , 1977. What day of the week was it?

2. Find the day of the week on 14th October 1989?

3. What was the day of the week on 3rd November 1978? a)Saturday b)Friday c) Monday d)Tuesday. 4. Vimal was born on 9th June 1975 the day on his birthday was? a)Monday b)Tuesday c)Wednesday d)Saturday 5. What day of the week was on independence day (15th august 1947)? a) Tuesday b)Thursday c)Friday d)Saturday. 6. Today is Sunday after 50 days it will be a) Wednesday b)Monday c)Friday d)Saturday 7. Today is Tuesday before 50days it was a) Sunday b)Monday c)Tuesday d)Wednesday 8. It was Friday on 17th Dec 1982, what will be the day on 22nd Sept 1984? 9. If it was Saturday on 17th Dec 1982.what was the week on 20th July 1979?

10.On what dates of Nov 2001 did Monday fall?

11. Prove that the calendar made for the year 1934 can serve for the year 1945?



12. If 09/12/2001 happens to be Sunday, then 09/12/2005 will be?

13. If 09/12/2001 happens to be Sunday, then 09/12/1971 would have been a?

14. On which of the following dates of May, 2005 did Tuesday fall?

15. How many days are there from 3rd Feb 1989 to 9th June 1989?

16. The year next to 1998 having the same calendar as that of 1998 is? a)2004 b)2003 c)2002 d)2005 17. On what dates of March 2006 will Sunday fall? a)5,12,19,26, b)7,14,21,28 c)3,10,17,24,31 d)6,13,20,27 18. The day on 5th March of a year is same day on what date of the same year? a)5th August b)5th October c)5th November d)5th December



Clocks

a) The dial of clock is divided in to 60 equal divided called minute space. b) 1 minute division =360/60=6 c) In one hour, the minute hand passes over 60 minute space and hour hand

goes over 5 minutes space. d) In every hour both the hand coincide once. e) When the hands of clocks are straight opposite to each other in direction ,

they are 30 minutes spaces apart and angle between them is of 180 .this happens once in every hour.

f) When both the hands are right angle they are 15 minutes space apart. This happens twice in every hour.

g) In one minute, angle moved by hour hand is ½ or (1/2) and angle moved by minute hand is 6.

h) Both the hands coincide after every 65 5/11 minutes.

1. Find the angle between the minute hand and hour hand of a clock. when the

time is 4.20?

2. At what time between 4 and 5 o’ clock will the hands of a clock be in the same straight line but not together?

3. The angle between the hands of a clock is maximum at

a)4 o’clock b)9 o’ clock c)6 o’ clock d)5 o’ clock?

4. The angle between the hands of a clock at 4 o’ clock is a)4 o’clock b)9 o’clock c)6 o’clock d)5 o’clock?

5. How many times will the hands of a clock cross each other in a day? a) 24 b)22 c)12 d)1 6. The angle between the minute hand and hour hand of the clock when the time is 6.40 is

a)60 b)100 c)80 d)40. 7. The angle between the minute hand and hour hand of the clock .when the time is 2.20 is



a)50 b)55 c)60 d)70

8 At what time between 3 and 4 o’clock are the hands of a clock together?

9 At the time between 7 and 8 o’clock at which the hands of a clock be in

straight opposite direction is

a) 54 6/11 minutes past 7 b)10 10/11 minutes past 7 c)5 5/11 minutes past 7 d)7:50

10 How many times do the hands of a clock are straight? A) 22 b) 24 c) 44 d) 48.

11. At what angle are the hands of a clock inclined when the time is 15 minutes past 5? a) 60 dec b)65 dec c) 67 ½ dec d) 75 dec 12. At what angles the hands of a clock are inclined when the time is 20 minutes past 7? a) 100 dec b) 80 dec c) 70 dec d) 60 dec 13. A clock is set right at 1 p.m it gains are minute an hour, when the clock indicates 6 p.m on the same day. The true time is a) 55 minutes past 5pm b) 55 5/61 minutes past 5pm c) 33 5/61 minutes past 5pm d) 5 5/143 minutes past 5pm 14. Clock. A loses 2 minute a day and clock B gains 3 minutes per day. If clock B is 10 minutes ahead of clock A how many days will it take clock B to be 30 minutes ahead of clock A? 15. A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day, when the watch indicated quarter past 4 o’ clock. Find the true time.



16. A watch slows down by 3 minutes in one day. After one day, the percentage error in time shown by the watch is a) 5/24% b) 6/24% c) 50/3% d) 20/3% 17. Clock X loses 1 minute a day and clock y gains 3 minutes per day. If clock y is 15 minutes ahead of clock x, how many days will it take clock. Y to be 35 minutes ahead of clock x? a) 2 b) 3 c) 4 d) 5



NUMBER & LETTER SERIES.

Start off with these simple series of numbers. Number series questions measure

your ability to reason without words.To answer these questions,you must determine the

pattern of the numbers in each series before you will be able to choose which number

comes next. These questions involve only simple arithmetic. Although most number series

items progress by adding or sub- tracting,some questions involve simple multiplication or

division. In each series, look for the degree and direction of change between the numbers.

In other words, do the numbers increase or decrease, and by how much?

1. Look at this series: 2, 4, 6, 8, 10, ... What number should come next?

a. 11 b. 12 c. 13 d. 14

2. Look at this series: 58, 52, 46, 40, 34, . . . What number should come next?

a. 26 b. 28 c. 30 d. 32


a. 40 b. 44 c. 54 d. 61

4. Look at this series: 544, 509, 474, 439, . . . What number should come next?

a. 404 b. 414 c. 420 d. 445

5. Look at this series: 201, 202, 204, 207, . . . What number should come next?

a. 205 b. 208 c. 210 d. 211


a. 9 b. 29 c. 32 d. 34


a. 20 b. 25 c. 30 d. 50


a. 20 b. 22 c. 23 d. 26

9. Look at this series: 22, 21, 23, 22, 24, 23, . . . What number should come next?

a. 22 b. 24 c. 25 d. 26




a. 7 b. 10 c. 14 d. 15


a. 15 b. 14 c. 13 d. 12


a. 14 b. 15 c. 21 d. 23


a. 12 b. 14 c. 27 d. 53

14. Look at this series: 2, 6, 18, 54, ...What number should come next?

a. 108 b. 148 c. 162 d. 216

15. Look at this series: 1,000, 200, 40, . . . What number should come next?

a. 8 b. 10 c. 15 d. 20


a. 7 b. 10 c. 12 d. 13


a. 52 b. 56 c. 96 d. 128

18. Look at this series: 1.5, 2.3, 3.1, 3.9, . . . What number should come next?

a. 4.2 b. 4.4 c. 4.7 d. 5.1

19. Look at this series: 5.2, 4.8, 4.4, 4, . . . What number should come next?

a. 3 b. 3.3 c. 3.5 d. 3.6

20. Look at this series: 2, 1, 1 /2 , 1/ 4,...What number should come next?

a. 1 /3 b. 1/ 8 c. 2/ 8 d. 1 /1 6

This set contains additional, and sometimes more difficult, number series questions.

Again, each question has a definite pattern. Some of the number series may be interrupted

by a particular number that appears periodically in the pattern. For example, in the series

14, 16, 32, 18, 20, 32, 22, 24, 32, the number 32 appears as every third number. Sometimes,



the pattern contains two alternating series. For example, in the series 1, 5, 3, 7, 5, 9, 7, the

pattern is add 4, subtract 2, add 4, subtract 2, and so on. Look carefully for the pattern,

and then choose which pair of numbers comes next. Note also that you will be choosing

from five options instead of four.

21. 84 78 72 66 60 54 48

a. 44 34 b. 42 36 c. 42 32 d. 40 34 e. 38 32

22. 3 8 13 18 23 28 33

a. 39 44 b. 38 44 c. 38 43 d. 37 42 e. 33 38

23. 20 20 17 17 14 14 11

a. 8 8 b. 11 11 c. 11 14 d. 8 9 e. 11 8

24. 18 21 25 18 29 33 18

a. 43 18 b. 41 44 c. 37 18 d. 37 41 e. 38 41

25. 9 11 33 13 15 33 17

a. 19 33 b. 33 35 c. 33 19 d. 15 33 e. 19 21

26. 2 8 14 20 26 32 38

a. 2 46 b. 44 50 c. 42 48 d. 40 42 e. 32 26

27. 28 25 5 21 18 5 14

a. 11 5 b. 10 7 c. 11 8 d. 5 10 e. 10 5

28. 9 12 11 14 13 16 15

a. 14 13 b. 18 21 c. 14 17 d. 12 13 e. 18 17

29. 75 65 85 55 45 85 35

a. 25 15 b. 25 85 c. 35 25 d. 85 35 e. 25 75

30. 1 10 7 20 13 30 19

a. 26 40 b. 29 36 c. 40 25 d. 25 31 e. 40 50

31. 10 20 25 35 40 50 55

a. 70 65 b. 60 70 c. 60 75 d. 60 65 e. 65 70



32. 40 40 31 31 22 22 13

a. 13 4 b. 13 5 c. 4 13 d. 9 4 e. 4 4

33. 17 17 34 20 20 31 23

a. 26 23 b. 34 20 c. 23 33 d. 27 28 e. 23 28

34. 2 3 4 5 6 4 8

a. 9 10 b. 4 8 c. 10 4 d. 9 4 e. 8 9

35. 61 57 50 61 43 36 61

a. 29 61 b. 27 20 c. 31 61 d. 22 15 e. 29 22

36. 9 16 23 30 37 44 51

a. 59 66 b. 56 62 c. 58 66 d. 58 65 e. 54 61

37. 8 22 12 16 22 20 24

a. 28 32 b. 28 22 c. 22 28 d. 32 36 e. 22 26

38. 6 20 8 14 10 8 12

a. 14 10 b. 2 18 c. 4 12 d. 2 14 e. 14 14

39. 11 16 21 26 31 36 41

a. 47 52 b. 46 52 c. 45 49 d. 46 51 e. 46 52

40. 8 11 21 15 18 21 22

a. 25 18 b. 25 21 c. 25 29 d. 24 21 e. 22 26

This set will give you additional practice dealing with number series questions.

41. 44 41 38 35 32 29 26

a. 24 21 b. 22 19 c. 23 19 d. 29 32 e. 23 20

42. 6 10 14 18 22 26 30

a. 36 40 b. 33 37 c. 38 42 d. 34 36 e. 34 38

43. 34 30 26 22 18 14 10

a. 8 6 b. 6 4 c. 14 18 d. 6 2 e. 4 0



44. 2 44 4 41 6 38 8

a. 10 12 b. 35 32 c. 34 9 d. 35 10 e. 10 52

45. 32 29 26 23 20 17 14

a. 11 8 b. 12 8 c. 11 7 d. 32 29 e. 10 9

46. 14 14 26 26 38 38 50

a. 60 72 b. 50 62 c. 50 72 d. 62 62 e. 62 80

47. 8 12 9 13 10 14 11

a. 14 11 b. 15 12 c. 8 15 d. 15 19 e. 8 5

48. 4 7 26 10 13 20 16

a. 14 4 b. 14 17 c. 18 14 d. 19 13 e. 19 14

49. 3 8 10 15 17 22 24

a. 26 28 b. 29 34 c. 29 31 d. 26 31 e. 26 32

50. 17 14 14 11 11 8 8

a. 8 5 b. 5 2 c. 8 2 d. 5 5 e. 5 8

51. 13 29 15 26 17 23 19

a. 21 23 b. 20 21 c. 20 17 d. 25 27 e. 22 20

52. 16 26 56 36 46 68 56

a. 80 66 b. 64 82 c. 66 80 d. 78 68 e. 66 82

53. 7 9 66 12 14 66 17

a. 19 66 b. 66 19 c. 19 22 d. 20 66 e. 66 20

54. 3 5 35 10 12 35 17

a. 22 35 b. 35 19 c. 19 35 d. 19 24 e. 22 24

55. 36 31 29 24 22 17 15

a. 13 11 b. 10 5 c. 13 8 d. 12 7 e. 10 8



56. 42 40 38 35 33 31 28

a. 25 22 b. 26 23 c. 26 24 d. 25 23 e. 26 22

57. 11 14 14 17 17 20 20

a. 23 23 b. 23 26 c. 21 24 d. 24 24 e. 24 27

58. 17 32 19 29 21 26 23

a. 25 25 b. 20 22 c. 23 25 d. 25 22 e. 27 32

59. 10 34 12 31 14 28 16

a. 25 18 b. 30 13 c. 19 26 d. 18 20 e. 25 22

60. 32 31 32 29 32 27 32

a. 25 32 b. 31 32 c. 29 32 d. 25 30 e. 29 30

This set contains additional number series questions, some of which are in Roman

numerals.These items differ from Sets 1,2,and 3 because they ask you to find the number

that fits somewhere into the middle of the series.Some of the items involve both numbers

and letters; for these questions, look for a number series and a letter series. (For

additional practice in working letter series questions, see Set 5.)

61. Look at this series: 8, 43, 11, 41, __, 39, 17, . . . What number should fill in the blank?

a. 8 b. 14 c. 43 d. 44

62. Look at this series: 15, __, 27, 27, 39, 39, . . . What number should fill the blank?

a. 51 b. 39 c. 23 d. 15

63. Look at this series: 83, 73, 93, 63, __, 93, 43, . . . What number should fill the blank?

a. 33 b. 53 c. 73 d. 93

64. Look at this series: 4, 7, 25, 10, __, 20, 16, 19, . . . What number should fill the blank?

a. 13 b. 15 c. 20 d. 28

65. Look at this series: 72, 76, 73, 77, 74, __, 75, . . . What number should fill the blank?

a. 70 b. 71 c. 75 d. 78



66. Look at this series: 70, 71, 76, __, 81, 86, 70, 91, . . . What number should fill the blank?

a. 70 b. 71 c. 80 d. 96

67. Look at this series: 664, 332, 340, 170, __, 89, . . . What number should fill the blank?

a. 85 b. 97 c. 109 d. 178

68. Look at this series: 0.15, 0.3, __, 1.2, 2.4, . . . What number should fill the blank?

a. 4.8 b. 0.006 c. 0.6 d. 0.9

69. Look at this series: 1 9 , 1 3 , 1, __, 9, . . . What number should fill the blank?

a. 2 3 b. 3 c. 6 d. 27

70. Look at this series: U32, V29, __, X23, Y20, . . . What number should fill the blank?

a. W26 b. W17 c. Z17 d. Z26

71. Look at this series: J14, L16, __, P20, R22, . . . What number should fill the blank?

a. S24 b. N18 c. M18 d. T24

72. Look at this series: F2, __, D8, C16, B32, . . . What number should fill the blank?

a. A16 b. G4 c. E4 d. E3

73. Look at this series: V, VIII, XI, XIV, __, XX, . . . What number should fill the blank?

a. IX b. XXIII c. XV d. XVII

74. Look at this series: XXIV, XX, __, XII, VIII, . . . What number should fill the blank?

a. XXII b. XIII c. XVI d. IV

75. Look at this series: VI, 10, V, 11, __, 12, III, . . . What number should fill the blank?

a. II b. IV c. IX d. 14



Coding-Decoding

Coding is a method of transmitting a message between the sender and the receiver

that no third person can understand it. The coding and decoding one’s ability of

deciphering the rule and breaking the code to decipher the message will be tested to know.

Approach:

1) Observe alphabets or numbers given in the code keenly.

2) Find the sequence it follows whether it is ascending or descending.

3) Detect the rule in which the alphabets/numbers/words follow.

4) Fill the appropriate letter/number/word in the blank given.

Letter coding: Alphabets in a word are replaced by other alphabets according to a

specific rule to know its code. So the common rule should de detected first. Some examples

are given below:

1) ‘ZYXW’ as coded as ‘ABCD’ then ‘STUV’ is coded as...........

Answer: Z – A, Y– B, X – C, W – D V – E, U – F, T – G, S – H STUV = HGFE

Answer = HGFE Rule= front alphabet= back alphabet.

2) ‘ bcd’ is coded as ‘def’ then ‘True’ is coded as..........

Answer: b – d (+2) c – e (+2) d – f (+2) +2 letters are considered in this code. True – Vtwg

Answer = Vtwg.

3) ‘ Hyderabad ’ is coded as ‘Ixedszcze’ then ‘Chennai’ is coded as..............

Answer: H – I (+1) Y – X (1–) D – E (1+) E – D (1-) R – S (1+) A – Z (1–) B – C (1+) A – Z (1– )

D – E (1+) Here if we observe alternatively the letter increasing and one letter decreasing.

Chennai =dgfmozj

Answer = dgfmozj

Number coding: In this each alphabets or words are assigned to the numeric values we

should observe the given letters and the assigned values and use the same rule to find the

value to of given code. Some examples are given below:

1)Apple is coded as 25563, Rung is coded as 7148. Then purple is coded as



Answer: PURPLE – 517563

Answer = 517563.

2)In a language A is coded as 1, B is coded as 2, ….. then FACE is coded as

Answer: Then FACE = 6135

Answer = 6135.

3)PUSH is coded as 1234, ROUGH is coded as 65274. Then SOUP is coded as

Answer: SOUP = 3521

Answer = 3521.

Substitution: In this section an object names are substituted with different object

names. We should carefully trace the substituion and answer given question. Some

examples are given below:

1)‘book’ is coded as ‘pencil’, ‘pencil’ is coded as ‘mirror’, ‘mirror is coded as ‘book’. Then

what is useful to write on a paper?

Answer: Pencil is coded as mirror

Answer = mirror.

2)‘man is coded as ‘woman’, woman is coded as ‘girl’, ‘girl’ is coded as ‘boy’, ‘boy’ is coded

as ‘worker’ then 6 years female is known as?

Answer: 6 years female = girl, but ‘girl’ is coded as ‘boy’.

Answer = boy.

3)‘Reds’ are ‘blues’, ‘blues’ are ‘whites’, ‘whites’ are ‘yellows’, ‘yellows’ are ‘oranges’,

‘oranges’ are ‘pinks’, then what is the colour of the sky?

Answer: Sky is blue, but blues are whites

Answer = white.

Exercise questions

1.In a certain code, COMPUTER is written as RFUVQNPC. How is MEDICINE written in the

same code ?

a) MFEDJJOE b) EOJDEJFM c) MFEJDJOE d)EOJDJEFM



Ans: Option d The letters of the word are written in reverse order and expect the first and

the last letter all other letters are move one step forward

2.In a code language, A is written as B, B is written as C, C is written as D and so on, then

how will SMART be written in that code language ?

a) TLBSU b)SHBSU c)TNBSU d)SNBRU

Ans: Option c The letters are coded by moving them 1 step forward.

3.In a certain code , RIPPLE is written as 613382 and LIFE is written as 8192. How is

PILLER written in that code?

a)318826 b)776655 c)786543 d)156724

Ans: Option a: Word : R I P P L E L I F E P I L L E R Code : 6 1 3 3 8 2 8 1 9 2 3 1 8 8 2 6

4.In a certain code FLOWER is coded as 36 and SUNFLOWER is coded as 81, then how to

code FOLLOWS?

a) 42 b)49 c)63 d) 36

Ans: Option b The word FLOWER has 6 letters . 62 is 36 The word SUNFLOWER has 9

letters. 92 is 81 Like FOLLOWS has 7 letters. So 72 is 49

5.In a certain code ,'il be pee' means 'roses are blue','sik hee' means 'red flowers' and 'pee

mit hee' means 'flowers are vegetables', How is 'red' written in that code?

a)hee b)sik c)be d)cannot be determined e)none

Ans: Option b Code Sentence Il be pee roses are blue Sik hee red flowers Pee mit hee

flowers are vegetables In II and III code ‘hee’ stands for ‘flowers’. So ‘sik’ stands for ‘red’

6.In a certain code language : ‘dugo hui mul zo’ stans for ‘work is very hard’ ‘hui dugo ba ki’

for ‘Bingo is very smart’; ‘nano mul dugo’ for ‘cake is hard’; and ‘mul ki gu’ for ‘smart and

hard’ Which of the following word stand for Bingo ?

a) Jalu b) Dugo c) Ki d) Ba

Ans: Option d Code Sentence 1.dugo hui mul zo work is very hard 2.hui dugo ba ki bingo is

very smart 3.nano mul dugo cake is hard 4.mul ki gu smart and hard

From second code and its sentence neither ‘ba’ is repeated nor is ‘Bingo.

7.If rain is called water, water is called air, air is called cloud, cloud is called sky, sky is

called sea, sea is called road, where do the aeroplanes fly ?



a) Water b) Road c) Sea d) Cloud

Ans: Option c Aeroplanes fly in sky and as per given codes sky is sea

8.If Orange is called Lemon, Lemon is called Flower, Flower is called Fish, Fish is called Tail

and Tail is called Pen, what is Rose ?

a) Pen b) Lemon c) Flower d) Fish

Ans: Option d Rose is a flower and as per given codes flower is fish.

9.In a certain code language $#* means ‘Shirt is clean’, @ D# means ‘Clean and neat’ and @

? means ‘neat boy’, then what is the code for ‘and’ in that language

a) # b) D c) @ d) Data inadequate

Ans: Option b Code sentence $#* ‘Shirt is clean’, @ D# ‘Clean and neat’ @ ? ‘neat boy’ Here

# stands for clean and @ stands for neat. D stands for ‘and’

10.If A stands for +, B stands for -, C stands for x, what is the value of (10C4)(A) (4C4)B6 ?

a) 60 b) 50 c) 56

d) 46 Ans: Option b (10C4)(A) (4C4)B6 = (10 * 4) + (4*4) –6 = 50

Exercise Questions

1. In a certain code language if the word ‘MUSEUM’ is coded as ‘LSPAPG’, then how will the

word ‘PALACE’ be coded in that language?

a. OYIWXY b. OYIXYW c. IYXYWO d. YXWYOI

2. If DELHI is coded as 73541 and CALCUTTA as 82589662, how can CALICUT be coded?

a. 5279431 b. 5978213 c. 8251896 d. 8543691

3. In a certain code language, if the number 1 is assigned to all the letters in odd numbered

places in the alphabet and the remaining letters are assigned the number 2, than what is

the code for the word ‘DANCE’?

a. 21211 b. 12121 c. 22111 d. 21121

4. In a certain code language, if the value of CONTRACT = 56 and ‘GROWTH’ = 30, then what

is the value of DISTRIBUTION?

a. 130 b. 132 c. 140 d. 142



5. In a certain code language, if the value of ‘BLOCK’ = 13 and ‘CURTAIN’ = 27, then what is

the value of the word ‘SCIENCE’?

a. 32 b. 36 c. 38 d. 34

6. In a certain code language, if the word ‘DISTANCE’ is coded as EDCINSAT, then how will

you code ‘ACQUIRE’ in that language?

a. EACIQUR b. EACRIUQ c. ERCIAQU d. EARCIQU

7. In a certain code language, if the value of 28 + 14 = 50 and 36 + 43 = 63, then what is the

value of 44 + 52 =?

a. 54 b. 56 c. 58 d. 62

8. In a certain code language, if the value of 14 x 15 = 25 and 26 x 42 = 64, then what is the

value of 73 x 31 = ?

a. 100 b. 110 c. 90 d. 120

9. In a certain code language, ‘kew xas huma deko’ means ‘she is eating apples’; ‘kew tepo

qua’ means ‘she sells toys’ and ‘sul lim deko’ means ‘I like apples’. Which word in that

language means ‘she’ and ‘apples’?

a. xas & deko b. xas & kew c. kew & deko d. kew & xas

10. These questions are based on a certain code language. Understand the logic in the

coding and answer the following questions.

PROCESSOR is coded as D4F3C5C1E1S1S1E3C6

a. QUADRANT

• Q1C7A1B2F6A1B7E4 • Q1D6A1B2F3A1B7E4 • Q1C7A1B2F3A1B7E4 •

Q1C7A1D2C6A1B7E5

b. WINDOW

• W1E4B7B2E3W1 • W1C3B7B2E3W1 • W1C3B7B2C3W1 • W1C3G7B2E3W1

Answer & Explanations

1. Exp: Word: M U S E U M

Logic: -1 -2 -3 -4 -5 -6



Code: L S P A P G

Similarly, the code for PALACE is

Word: P A L A C E

Logic: -1 -2 -3 -4 -5 -6

Code: O Y I W X Y

2. Exp: The alphabets are coded as follows:

D E L H I C A U T

7 3 5 4 1 8 2 9 6

So, in CALICUT, C is coded as 8, A as 2, L as 5, U as 9 and T as 6. Thus, the code for

CALICUT is 8251896.

3. Exp: The code for the word DANCE is 21211.

4. Exp: Number of letters in the word CONTRACT = 8 and 8 x 7 = 56.

Number of letters in the word GROWTH = 6 and 6 x 5 = 30.

Similarly, DISTRIBUTION => 12 and 12 x 11 = 132.

5. Exp: In this product of the digits in the place-values of the letters as per the alphabet is

obtained first and then added i.e, BLOCK

=> B = 2

L = 12 => 1 x 2 = 2

O = 15 => 1 x 5 = 5

C = 3

K = 11 => 1 x 1 = 1

Now (2 + 2 + 5 + 3 + 1) = 13.

So, BLOCK = 13.

Similarly, SCIENCE = 38.



6. Exp: In this coding, the letters from either end of the word are written, first a letter from

the right end and then a letter from the left end of the word and so on. Hence DISTANCE is

coded as EDCINSAT.

Similarly, ACQUIRE is coded as EARCIQU.

7. Exp: It is given that 28 + 14 = 50 => (2 + 8) x (1 + 4)

=> 10 x 5 = 50 and 36 + 43 = 63 => (3 + 6) x (4 + 3)

=> 9 x 7 = 63 then 44 + 52 => (4 + 4) x (5 + 2) => 8 x 7 = 56.

8. Exp: 14 x 15 = 14 + 15 = 29 and 29 – 4 = 25.

26 x 42 = 26 + 42 = 68 and 68 – 4 = 64.

Similarly, 73 x 31 = (73 + 31) – 4 = 104 – 4 = 100.

9. Exp: In the first and second statements, the common code word is ‘kew’ and the common

word is ‘she’. So, ‘kew’stands for ‘she’.

In the first and third statements, the common code word is ‘deko’ and the common

word is ‘apples’. So, ‘deko’stands for ‘apples’.

10. a. Exp: PROCESSOR =>

P = 16 and D4 => 4 x 4 = 16 = P

R = 18 and F3 => 6 x 3 = 18 = R

O = 15 and C5 => 3 x 5 = 15 = O and so on.

Hence, PROFESSOR is coded as D4F3C5C1E1S1S1E3C6.

QUADRANT is coded as Q1C7A1B2F3A1B7E4.

b. Exp: WINDOW is coded as W1C3B7B2E3W1.



DIRECTION SENSE

Definition :

The Adjoining figures show the four main directions ( North N, South S, East E, West W) and

Four cardinal directions ( North East NE, North West NW, South East SE, South West SW ) to help the candidates know the directions.

1. A man is facing west. He turns 45 degree in the clockwise direction and then another 180 degree in the same direction and then 270 degree in the anticlockwise direction. Find which direction he is facing now ?

1. South-West 2. West 3. South 4. East-South

2. A man is facing north. He turns 45 degree in the clockwise direction and then another 180 degree in the same direction and then 45 degree in the anticlockwise direction. Find which direction he is facing now ?

1. North 2. East 3. West 4. South



3. One day, Raviraj left home and cycled 20 Km southwards, turned right and cycled 10 km and turned right and cycled 20 Km and turned left and cycled 20 Km. How many kilometres will he have to cycle to reach his home straight ?

1. 50 Km 2. 30 Km 3. 40 Km 4. 60 Km

4. A child is looking for his father. He went 90 meters in the east before turning to his right. He went 20 meters before turning to is right again to look for his father at his uncle's place 30 meters from this point. His father was not there. From there, he went 100 meters to his north before meeting his father in a street. How far did the son meet his father from starting point ?

1. 80 metre 2. 90 metre 3. 100 metre 4. 110 metre

5. Kunal walks 10 km towards North. From there he walks 6 Km towards South. Then, he walks 3 Km towards east. How far and in which direction is he with reference to his starting point ?

1. 5 Km North 2. 5 Km South 3. 5 Km East 4. 5 Km North-East

6. Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ?

1. 40 metres 2. 50 metres 3. 60 metres 4. 70 metres

7. A dog runs 20 metre towards East and turns Right, runs 10 metre and turns to right, runs 9 metre and again turns to left, runs 5 metre and then turns to left, runs 12 metre and finally turns to left and runs 6 metre. Now which direction dog is facing ?

1. East 2.North 3.West 4.South



BLOOD RELATION

1.Pointing to a photograph of a boy Suresh said, "He is the son of the only son of my mother."

How is Suresh related to that boy?

A. Brother B. Uncle

C. Cousin D. Father

Answer: Option D

The boy in the photograph is the only son of the son of Suresh's mother i.e., the son of Suresh. Hence,

Suresh is the father of boy.

2.If A + B means A is the mother of B; A - B means A is the brother B; A % B means A is the

father of B and A x B means A is the sister of B, which of the following shows that P is the

maternal uncle of Q?

A. Q - N + M x P B. P + S x N - Q

C. P - M + N x Q D. Q - S % P

3.If A is the brother of B; B is the sister of C; and C is the father of D, how D is related to A?

A. Brother B. Sister

C. Nephew D. Cannot be determined

4. Pointing to a man, a woman said, "His mother is the only daughter of my mother". How is the

woman related to man?

(1) Mother (2) Grandmother (3) Sister (4) Daughter (5) None of these

5. Pointing to a man, a woman said, "His mother is the daughter of my mother's only daughter,

How is the man related to that woman?

(l)Son (2) Father (3) Brother (4) Grandson (5) None of these

6. Pointing towards Waman, Madhav said "I am the only son of his father's one of the sons".

How Waman is related to Madhav?

(1) Nephew (2) Uncle (3) Either father or uncle (4) Father (5) None of these

7. Pointing to a man in the photograph, a woman said, "He is the only son of my mother's

father". How is the woman related to the man in the photograph?

(1) Niece (2) Sister (3) Mother (4) Daughter (5) None of these















8. Pointing to a gentleman, Deepak said, "His only brother is the father of my daughter's father",

How is the gentleman related to Deepak?

(1) Father (2) Grandfather (3) Uncle (4) Brother-in-law (5) None of these

9. Pointing towards Neeru, Asha said, "I am the only daughter of her mother's son". How is

Neeru related to Asha?

(l)Aunt ' (2) Cousin (3) Niece (4) Mother (5) None of these

10. If Neha says, "Amruta's father Raj is the only son of my father-in-law, Mahesh"; then how

Bindu, who is sister of Amruta, is related to Mahesh?

(1) Daughter (2) Wife (3) Daughter-in-law (4) Niece (5) None of these

11. Pointing towards a photograph of a girl, Rajan said, "She has no sisters or daughters but her

mother is the only daughter of my mother".

How is the girl in the photograph related to Rajan's mother?

(1) Sister-in-Law (2) Granddaughter (3) Daughter-in-Law (4) Cannot be determined (5) None of

these

12. Pointing towards a person in a photograph, Raman said, "She is the only daughter of the

mother of my brother's sister". How is the person in photograph related to Raman?'

(1) Daughter (2) Sister . (3) Wife (4) Cousin (5) None of these.

13. Pointing to a man in a photograph, a woman said, "His brother's father is the only son of my

grandfather". How is the woman related to the man in the photograph?

(1) Sister (2) Mother (3) Grandmother (4) Aunt (5) Daughter



SEATING ARRANGEMENT

1. P, Q, R, S, T, U, V & W are eight friends sitting around a circle facing towards

the centre. i) W is to the immediate left of P but is not the neighbour of T and S ii)

U is to the immediate right of Q and V is neighbour of T iii) R is between T and U

A. What is the position of V?

a. To the immediate right of W

b. Between T and R

c. Third to the right of U

d. Second to the left of S

e. None of these

B. What is the position of S?

a. Between Q and U

b. To the immediate left of P

c. Second to the right of U

d. To the immediate left of Q

e. None of these

C. Which of the following statements is true?

a. U is the neighbour of V

b. V is between W and T

c. W is between P and S

d. T is between U and Q

e. None of these

Answers: 1-c, 2-d, 3-b

2. Eight friends P, M, R, T, Q, U, V & W are sitting in two opposite rows, facing

each other. Each row has 4 persons. P is between U and V and is facing North. W

is opposite to Q who is to the immediate left of M. R is between T and M. W is to

the immediate right of V.



A. Who is to the immediate right of R?

a. M b. U c. M or T d. Cannot be determined e. None of these

B. Which of the following pairs has the person sitting opposite each other?

a. MV b. RV c. TV d. UR e. None of these

C. Four of the following five are alike in a certain way on the basis of their

positions and so form a group. Which is the one that does not belong to the

group?

a. TP b. RV c. QP d. QV e. MW

D. Which of the following pairs of persons has second person sitting to the

immediate left of the first person?

a. UP b. VP c. QM d. RT e. None of these

E. Who is sitting opposite of R?

a. U b. Q c. V d. P e. None of these

Answers: 1-e, 2-a, 3-c, 4-b, 5-d

3. A, B, C, D, E, F, G and H are sitting around a circle, facing the centre. A sits

fourth to the right of H while second to the left of F. C is not the neighbor of F and

B. D sits third to the right of C. H never sits next to G.

A. Who among the following sits between B and D?

a. G b. F c. H d. A e. C

B. Which of the following pairs sit between H and G?

a. BH b. EF c. CE d. DB e. None of these

C. Four of the following five are alike in a certain way based on their

positions in the seating arrangement and so form the group. Which is the

one that does not belong to that group?

a. AE b. HF c. BD d. GE e. CH

D. Who is to immediate right of A?

a. C b. D c. G d. Data inadequate e. None of these

E. Who sits second to the right of B?

a. A b. C c. D d. E e. None of these

F. Which is the position of B with respect to C?

I. Second to the right

II. Sixth to the left



III. Third to the left

IV. Fifth to the right

a. Only II

b. Only II and III

c. Only I and IV

d. Data inadequate

e. Both III and IV

Answers: 1-b, 2-c, 3-a, 4-b, 5-d, 6-e

4. A, B, C, D, E, F, G and H are sitting around a circle facing at the centre. G is

fourth to the right of A who is second to the right of D. E is second to the right of

C who is not an immediate neighbour of G or D. B is second to the right of F.

a. In which of the following pairs is the first person sitting to the

immediate right of the second person?

a. EG b. GF c. HE d. BD e. None of these

b. Who is third to the left of H?

a. A b. D c. B d. Data inadequate e. None

c. Who is the second to the right of H?

a. E b. G c. F d. Data inadequate e. None

d. What is F's position with respect to C?

1. Fourth to the left

2. Fifth to the left

3. Fourth to the right

4. Third to the right

a. Only 1 b. Only 2 c. Only 1 and 4 d. Only 2 and 3

e. Only 1 and 3

e. Who is the immediate right of G?

a. F b. G c. D d. Data inadequate e. None

Answers: 1-d, 2-c, 3-b, 4-e, 5-a



5. Mohan and Suresh study in the same class. Mohan has secured more marks

than Suresh in the terminal examination. Suresh's rank is seventh from top

among all the students in the class. Which of the following is definitely true?

A. Mohan stood first in the terminal examination

B. There is at least one student between Mohan and Suresh in the rank list

C. There are at the most five students between Mohan and Suresh in the rank

list

D. Suresh is five ranks lower than Mohan in the rank list

E. None of these

Answer: C

6. In a row of girls facing North, Rinky is 10th to the left to Pinky who is 21st

from the right end. If Minky who is 17th from the left end is 4th to the right of

Rinky. How many girls are there in the row?

A. Data inadequate

B. 44

C. 37

D. 43

E. None of these

Answer: D

7. In a row of 40 girls, when Kamal was shifted to her left by 4 places her number

from the left end of the row became 10. What was the number of Sujata from the

right end of the row if Sujata was three places to the right of Kamal's original

position?

A. 22

B. 26

C. 25

D. 23

E. None of these

Answer: D

8. Akshay is 16th from the left end in the row of boys and Vijay is 18th from the

right end. Avinash is 11th from Akshay towards the right end and 3rd from



Vijay towards the right end. How many boys are there in the row?

A. Data inadequate

B. 42

C. 40

D. 48

E. None of these

Answer: E( Answer is 41)

9.In a row of thirty boys, R is fourth from the right end and W is tenth from the

left end. How many boys are there between R and W?

A. 15

B. 16

C. 17

D. Data inadequate

E. None of these

Answer: B

10. Study the following five numbers and answer the questions given below: 517

325 639 841 792

A. What will be last digit of the third number from top when they are

arranged in descending order after reversing the position of the digits within

each number?

a. 7 b. 3 c. 5 d. 2 e. None of these

B. What will be the middle digit of the second lowest number after the

position of only the first and the second digits within each number are

interchanged?


C. What will be the first digit of the second highest number after the position

of only the second and the third digits within each number are interchanged?


Answers: 1-b, 2-d, 3-a

quantitative and reasoning aptitude prepared by : …

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