4. ratio & proportion & average

8/18/2019 4. Ratio & Proportion & Average

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Abhyaas/Skill School/Math/RPA www.abhyaas.in

Ratio & Proportion & Average

Session Objectives

Ratio and Proportion

Properties of Averages

1. A : B = 3 : 7 and the sum of A and B is 45. Find

the value of B.

A. 33.5 B. 31.5 C. 28 D. 36

2. Mean Proportional between 8 and 72 is

A. 24 B. 40 C. 16 D. 32

3. What must be added to each term of the fraction

4/9, so that it becomes 2/3?

A. 6 B. 11 C. 16 D. 1

4. What will be the fourth proportional to 3,15 and

27 is

A. 39 B. 135 C. 81 D. 45

5. The ratio of 43.5 : 25 is same as:

A. 2:1 B. 7:5 C. 2:9 D. 4:1

6. The ratio of A’s money to that of B’s money is

4:5 and B’s money to C’s money is 2:3. If A has

Rs. 800, then total amount of money among A,

B and C in Rs is:A. 3000 B. 3620 C. 3300 D. 2790

7. The number 68 is divided into two parts such

that one-seventh of the first part is equal to

one-tenth of the second part. Find the first part.

A. 7 B. 22 C. 28 D. 32

8. The sum of Rs. 530 is divided among A, B and

C such that A gets Rs. 70 more than B and B

gets Rs.80 more than C. What is the ratio of the amount with A to that of C?

A. 5:2 B. 7:4 C. 25:18 D. none

9. Two numbers are in the ratio 3:5. If 8 is

subtracted from each, they are in the ratio 1:3.

The second number is:

A. 15 B. 20 C. 4 D. 12

10. The total emoluments of P and Q are equal.

However, P gets 65% of the basic salary as

allowances and Q gets 80% of the basic salary

as allowances. What is the ratio of the basic

salaries of P & Q?

A. 16:13 B. 5:7 C. 12:11 D. 7:9

11. From each of two given numbers, half of smaller

number is subtracted. Of the resulting numbers,

the larger one is three times as large as the smaller.

What is the ratio of the two numbers?

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

12. A man buys spirit at Rs.60 per liter, adds water

to it and then sells it at Rs.75 per liter. What is

the ratio of spirit to water if his profit in the deal

is 37.5%?

A. 9:1 B. 10:1 C. 11:1 D. 11:2

13. An amount of money is distributed amongst A,

B and C such that A gets half that of B and B

gets twice that of C. What is the ratio between

the share of B to the sum of the shares of A and

B?

A. 4:3 B. 3:2 C. 2:3 D. 2:5

14. The ages of a man and his son are in the ratio of

7:2. After 15 yrs, their ages would be in the ratio

of 2:1. What was the father’s age when the son

was born?

A. 25 B. 35

C. 42 D. Data Inadequate

15. Brass is an alloy of Copper and Zinc with no

other metal in it. In a sample of Brass, Copper and Zinc are in the ratio of 13:7. How much

Copper will be there in a 500 kg sample of this

alloy?

A. 150 kg B. 175 kg

C. 325 kg D. 500 kg

16. The side of a square is increased by 50% of its

original measure. Find the ratio of the areas of

the original square to the new square.

A. 9:4 B. 4:9 C. 2:3 D. None


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17. A milkman mixes 20 litres of water with 80 litres

of Milk. After selling 1/4th of this mixture, he

adds water to replenish the quantity he has sold.

What is the current proportion of water to milk?

A. 7:12 B. 2:3 C. 3:2 D. 5:12

18. Three vessels having volumes in the ratios 2:3:4are full with spirit, alcohol and water in the ratios

of 1:1:1 in the first vessel, 1:2:3 in the second

vessel and 1:2:1 in the third vessel. If the liquids

in all the three vessels are emptied into a bigger

container, then what will be the ratio of spirit,

alcohol and water in the bigger container?

A. 13:22:19 B. 19:23:22

C. 14:18:7 D. None of these

19. In a school, 10% of total no. of boys is equal to¼ th of the girls. What is the ratio of boys to girls

in that school?

A. 5:4 B. 5:2 C. 2:1 D. 3:2

20. The incomes of A and B are in the ratio of 3:2

and their expenses are in the ratio of 5:3. If each

of them saves Rs.3000, then B’s income is:

A. 10000 B. 6000

C. 9000 D. 12000

21. The ages of A and B are in the ratio of 3:1. Fifteenyears hence, the ratio will be 2:1. Their present

ages are:

A. 30 yrs, 10 yrs B. 45 yrs, 15 yrs

C. 21 yrs, 7 yrs D. 60 yrs, 20 yrs.

22. In 80 L mixture of milk and water, milk and water

are in the ratio of 5:3. If 16 L of this mixture is

replaced by 16 L of milk then the ratio of milk

and water in the resulting mixture becomes:

A. 2:1 B. 6:3 C. 7:3 D. 8:3

23. In a mixture of 100 L, the ratio of milk and water

is 3:1. If 200 L of water is added to the mixture,

what will be the new ratio of milk and water?

A. 1:3 B. 5:6 C. 2:5 D. 5:2

24. Third proportional to 20 and 30 is

A. 40 B. 55 C. 60 D. 45

25. If a:b = 2:3 and b:c = 5:6, Find a:b:c?

A. 10:15:18 B. 20:30:36

C. Both A and B D. None of these.

26. A hare and a jackal are running a race. Three

leaps of the hare are equal to four leaps of the

jackal. For every six leaps of the hare, the jackal

takes 5 leaps. Find the ratio of their speeds.A. 64:25 B. 8:5 C. 5:8 D. 25:64

27. Parul purchased 150 kg of wheat at a rate of

Rs 7 per kg. She sold 50 kg at a profit of 10%.

At what rate should she sell the remaining wheat

to get a profit of 20% on the total deal?

A. Rs 7.5 B. Rs 7.7

C. Rs 8.75 D. Rs 8.5

28. How many litres of water must be added to acask which contains 40 L of milk at the rate of

Rs 3.5 per litre so that the cost of milk reduces

to Rs 2 per litre?

A. 25 B. 30 C. 35 D. None

29. A jar contains mixture of two liquids A and B in

the ratio 4:1. When 10 L of the mixture is

replaced with an equal amount of B the ratio

becomes 2:3. How many litres of liquid A were

contained in the jar?

A. 12 B. 20C. 16 D. Insufficient data

30. A trader has 50 kg of pulses, part of which he

sells at a profit of 8% and rest at 18% profit. He

gains 14% on the whole. What quantity is sold

at 18% profit?

A. 20 kg B. 30 kg C. 40 kg D. 10 kg

31. A person has chemical worth Rs 25 per litre. In

what ratio should water be mixed with that

chemical so that after selling the mixture at Rs

20 per litre he makes a profit of 25%

A. 1:4 B. 4:1 C. 16:9 D. 9:16

32. Two different alloys contain copper and iron in

the ratios of 5:8 and 5:3. Equal weights of alloys

are mixed to form a third alloy. What is the ratio

of copper and iron in the third alloy?

A. 103:105 B. 15:24

C. 105:103 D. 3:8


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33. A mixture of wine with 20L of water is worth

Rs.90 per litre. If pure wine is worth Rs.108

per litre, how much wine is there in the mixture?

A. 120 L B. 75 L C. 50 L D. 100 L

34. 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 weight of boys in the class.

A. 47.55 kg B. 48.55 kg

C. 48 kg D. 49.25 kg

35. The average of ten numbers is 7. Each number

is multiplied by 12, then 6 is added to each

number. At last each number is divided by 15.

The average of the new set of numbers is:

A. 6 B. 9 C. 10 D. 15

36. The mean of a, b, c is M and ab+bc+ca=0. The

mean of a2, b2,c2 is

A. M 2 B. 3M 2 C. 6M 2 D. 9M 2

37. If the mean of 5 observations x, x+2, x+4, x+6,

x+8 is 11, then the mean of the last three

observations is

A. 11 B. 13 C. 15 D. 17

38. The average age of 3 boys is 25 years and their

ages are in the ratio 3:5:7, the age of the youngest boy is

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

39. Rs 9700 has been divided among X,Y,Z such

that if their shares are reduced by Rs 30,Rs

20,Rs 50 then the balances are in the ratio 3:4:5.

What is Y’s share in Rs?

A. 3180 B. 3220

C. 3200 D. 3253.33

40. In 80L mixture of milk and water, milk and water

are in the ratio 5:3. If 16L of this mixture is

replaced by 16L of milk then the ratio of milk

and water in resulting mixture is

A. 2:1 B. 6:3 C. 7:3 D. 8:3

4. ratio & proportion & average

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