sample copy. not for distribution.9. alligation or mixture formulae 26 10. stock & share’s...

Sample Copy. Not For Distribution.

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Math’s Formulae


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Printed in India


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Math’s Formulae Competitive Exam & Academic Exam Reference Book

SumitShrivastava

EDUCREATION PUBLISHING

(Since 2011)

www.educreation.in


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About The Author

He was born in Rewa on 13 sep 1988. He

completed his schooling from Satna and then

went to Indore for further studies. He completed

his Graduation (B.com) from DAVV Indore &

Post Graduation (MBA Finance with

International business) from People’s Institute of

Management & Research Bhopal MP (India).

After that he attempted many competitive

Examinations like SSC, Banking, Vyapam, Railway, Lic, GIC etc.

for government jobs. Unfortunately he was not selected for any of

those jobs. Then he analysed regarding his failure and found his

weakness in Maths.

He wrote many notes about maths formulas and now he wants

to share with all learners, with the help of the book. Presently he is

working with MNC as an Accounts Executive.

Note:-Dear members if you feel that this book needs any

improvement or something more can be added then please help the

Writer. Your suggestion or valuable comments are invited on

[email protected].

*****


mailto:[email protected]

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About The Book

This book is for those students who want to learn maths formulae

or we can say for those learners who prepare for competitive

exams like Banking ,Railway ,SSC ,LIC ,GIC , Vyapametc,

I have written this book because, I experienced that during

examination time, either it is competitive Exam or Academic

Exam, Students quit from the Arithmetic Aptitude or Math’s

questions. Mostly it happens because students forget the formulae.

To help and motivate students, I covered maximum formulae like

Train’s Formulae, Time & Work Formulae, Profit & loss

Formulae, Average Formulae, Permutation & combination

Formulae, HCF & LCF Formulae , Square Root & Cube Root

Formulae, Alligation or Mixture Formulae , Stock & Share’s

Formulae, Time & distance Formulae, Simple Interest Formulae,

Partnership Formulae, Calendar Formulae, Area’s Formulae,

Algebra Formulae, Decimal Fraction Formulae, Surds & Indices

Formulae, Pipes & Cistern Formulae, Probability Formulae,

Compound Interest Formulae, Percentage Formulae, Clock

Formulae, Boats & Stream’s Formulae, Logarithm, Problems on

Ages, Height & Distance, Simplification, Ratio and Proportion,

True Discount ,Discount, Polygon Properties, Volume & Surface

Area ,Circle Formulae, Perimeter Formulae, Roman Number,

Square Root & Cube Roots.

I have facilitated some examples on some formulas which will

help learners to understand and implement while solving sums. I

hope the content of this book will surely help the learners. This

book is only for reference.

Recommendation:- Please read this book once before attempting

any exam containing Arithmetic Aptitude.

“Math’s is like a game when Formula is in your Brain”

*****


http://www.indiabix.com/aptitude/questions-and-answers/

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Dedicated To

My Lovely Parents Shri Ramesh Kumar Shrivastava(Father) S/o Late Mr. KaushalPd.Shrivastava (grandfather) &SmtSunitaShrivastava (Mother).

They provided me everything in my life. They carried me on their shoulders and encouraged me to touch the sky and made my dream come true.

They never let me down and hold in every ups & Downs of life at every movement and showed right path.

And my two lovely sisters helped and directed me always. My elder sister Mrs.Reena Nigam &

Younger one MrsAkshitaShrivastava, Both is lecturers by profession.

I would like to thank all of them to be a part of my life.

And thanks to god because each and every movement give by you without you I am unable to walk a single step in this life.

*****


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Content List

S.no. Content Page

1. Numbers 1

2. Problem on Train’s Formulae 6

3. Time & Work Formulae 9

4. Profit & loss Formulae 12

5. Average Formulae 15

6. Permutation & combination Formulae 17

7. HCF & LCF Formulae 21

8. Square Root & Cube Root Formulae 24

9. Alligation or Mixture Formulae 26

10. Stock & Share’s Formulae 29

11. Time & distance Formulae 31

12. Simple Interest Formulae 33

13. Partnership Formulae 35

14. Calendar Formulae 36

15. Area’s Formulae 38

16. Algebra Formula 42

17. Decimal Fraction Formulae 45

18. Surds & Indices Formulae 49

19. Pipes & Cistern Formulae 50

20. Probability Formulae 51

21. Compound Interest Formulae 54

22. Percentage Formulae 57


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23. Clock Formulae 60

24. Boats & Stream’s Formulae 62

25. Logarithm 65

26. Problems on Ages 67

27. Height & Distance 69

28. Simplification 72

29. Ratio and Proportion 75

30. True Discount 77

31. Discount 77

32. Polygon Properties 78

33. Volume & Surface Area 82

34. Circle Formulae 84

35. Perimeter Formulae 89

36. Roman Number 91

37. Square Root & Cube Roots 93

38. Short Cut Maths Tricks 97


SumitShrivastava

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Numbers

Important Facts and Formulae

1.Numbers:In Hindu –Arabic System, we use ten symbols,

namely 0,1,2,3,4,5,6,7,8 and 9 . We call them digits.

A number is denoted by a group of digits, called numeral.

Some numerals are given below in a place-value chart.

Ten

Crores Crores

Ten

Lacs Lacs

Ten

Thousands Thousands Hundreds Tens Units

i. 5

3 6 7 4 9

ii. 1 6

8 0 3 0 4

iii. 6 0 5

1 4 0 8 9

iv. 2 4 1 6

0 8 0 0 3

We write these numbers in words as :

I) Five lac thirty-six thousand seven hundred forty-nine.

II) Sixteen lac eighty thousand three hundred four.

III) Six crore five lac fourteen thousand eighty-nine.

IV) Twenty-four croresixteen lac eight thousand three.

2. FACE VALUE OF A DIGIT IN A NUMERAL.

The face value of a digit in a numeral is the value of the digit itself,

wherever it may be in the place value chart.

In the numeral 536749, the face value of 7 is 7, the face value of 6

is 6 the face value of 5 is 5 and so on.

3. PLACE VALUE OR LOCAL VALUE OF A DIGIT IN A

NUMERAL

In the numeral 536749, we have

Place value of 9 = (9x1) = 9;

Place value of 4 = (4x10)=40;


SumitShrivastava

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Place value of 7 = (7x100) = 700;

Place value of 6 = (6x1000)=6000;

Place value of 3 = (3x10000) = 30000;

Place value of 5 = (5x100000)=500000;

4.TYPES OF NUMBERS

Natural Numbers:-Counting numbers are called natural numbers.

Thus 1,2,3,4,5,6……………………….. etc. are all natural

numbers.

Whole Numbers:- All counting numbers together with zero form

the set of whole numbers.

Note:

i. 0 is a whole number which is not a natural numbers.

ii. Every natural numbers is a whole numbers.

Thus 0,1,2,3,4,5,6……………………………………………

… … ……… ………. Are whole numbers.

Integers:-All counting numbers, 0 and negative of counting

numbers are called integers.

a. Positive Integers: ( 1,2, 3,4,5………………………..) is the

set of positive integers.

b. Negative Integers: (-1,-2,-3,-4,-5…………………………..) is

the set of negative integers.

c. Non-Negative Integers: 0 is neither positive nor negative,

a. .‘. {O,1,2,3,4,5………} is set of non-negative integers.

d. Non-Positive Integers:

a. {0,-1,-2,-3,-4,…….} is set of non-positive integers.

Even Numbers:- A numbers divisible by 2 is called an even

number. Thus 0,2,4,6,8,10,………etc. are all even numbers.

Odd Numbers:- A number not divisible by 2 is called an odd

number . Thus 1,3,5,7,9,………..etc. are odd numbers..


SumitShrivastava

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Prime Numbers:- A number greater than 1 having exactly two

factors, namely 1 and itself is called a prime number.

Prime Numbers Upto 100 are:

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73

,79,83,89,97.

To Test Whether a given number p is prime: Let p be a

given number .find a whole number k >√p.

Take all prime numbers less than or equal to k.

If no one of these divides p exactly, we say that p is prime

.otherwise, P is not prime.

Composite Numbers:- Numbers greater than 1 which are not

prime , are called composite numbers e.g. 4,6,8,9,10,12 etc .

Note :-

i) 1 is neither prime number nor composite.

ii) 2 is the only even which is prime.

Co-Primes:- Two natural numbers a and b are said to be co-prime

if there HCF is 1 e.g. (2,3), (4,5), (7,9) (8,11) etc. are pairs of co-

primes.

Tests of Divisibility

i. Divisibility by 2 :- A number is divisible by 2 , if its unit digit is

any of 0,2,4,6,8.

Ex. 64892 is divisible by 2, While 64895 is not divisible by 2.

ii. Divisibility by 3 :- A number is divisible by 3 , Only when the

sum of its digit is divisible by 3.

Example.

(a) Consider the number 587421. Sum of its digit is 27, which

is divisible by 3, So 587421 is divisible by 3.

(b) Consider the number 689453. Sum of its digit is 35, which

is not divisible by 3, So 689453 is divisible by 3.


SumitShrivastava

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iii. Divisibility by 4 :- A number is divisible by 4 ,If the sum of its

last 2 digit is divisible by 4.

Example:-

(a) 5249376 is divisible by 4 , since 76 is divisible by 4.

(b) 638214 is not divisible by 4, since 14 is not divisible by 4.

iv. Divisibility by 5 :- A number is divisible by 5 ,If its unit digit is

5 or 0.

Example:-

(a) 328695 is divisible by 5.

(b) 947310 is divisible by 5.

(c) None of 507062,717554,656676,30578 is divisible by 5.

v. Divisibility by 6 :- A number is divisible by 6 ,If it is divisible

by both 2 and 3.

Example:-

(a) 974562 is divisible by 2 as well as 3 . So, it is divisible by

6.

(b) 975416 is not divisible by 6, since sum of its digits is 32,

which is not divisible by 3.

vi.Divisibility by 8 :- A number is divisible by 8 only when the

number formed by its last 3 digits is divisible by 8.

Example:-

(a) 6754120 is divisible by 8, since 120 is divisible by 8.

(b) 5943246 is not divisible by 8, since 246 is not divisible

by 8.

vii. Divisibility by 9 :- A number is divisible by 9 if the sum of its

digits is divisible by 9.

Example:-

(a) 594324 is divisible by 9 , since the sum of its digits is

27, which is divisible by 9.

(b) 3714529 is not divisible by 9 , since the sum of its

digits is 31, which is not divisible by 9.


SumitShrivastava

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viii. Divisibility by 10 :- A number is divisible by 10 only when

its unit digit is 0.

Example:-

(a) 234780 is divisible by 10 will 234785 is not divisible by

10

ix. Divisibility by 11:- A number is divisible by 11 , if the

difference of the sum of its digits at odd places and the sum of its

digits at even places is either 0 or a number divisible by 11.

Example:- 49235714 is divisible by 11 , since .

(Some of its digits at odd places) – (Some of its digits at even

places) is 11, which is divisible by 11.

An Important Note:- if a number N is divisible by two number a &

b , where a and b are co-primes , then N is divisible by ab.

SOME RESULTS ON DIVISION

(i) (xn - a

n) is divisible by ( x – a) for all values of n.

(ii) (xn + a

n) is divisible by ( x + a) for even values of n.

(iii) (xn + a

n) is divisible by ( x + a) for odd values of n.

Division Algorithm

If we divide a number by another number, then

Dividend = (Divisor X Quotient) + Remainder

*****


SumitShrivastava

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Problem on Train’s Formulae

1. km/hr to m/s conversion:

a km/hr =

a x 5

m/s. 18

2. m/s to km/hr conversion:

a m/s =

a x 18

km/hr. 5

3. Formulas for finding Speed, Time and Distance

4. Time taken by a train of length l metres to pass a pole or

standing man or a signal post is equal to the time taken by the

train to cover l metres.

5. Time taken by a train of length l metres to pass a stationery

object of length bmetres is the time taken by the train to cover

(l + b) metres.

6. Suppose two trains or two objects bodies are moving in the

same direction at um/s and v m/s, where u > v, then their

relative speed is = (u - v) m/s.

7. Suppose two trains or two objects bodies are moving in

opposite directions at um/s and v m/s, then their relative speed

is = (u + v) m/s.

8. If two trains of length a metres and b metres are moving in

opposite directions atu m/s and v m/s, then:

The time taken by the trains to cross each other = (a + b)

sec. (u + v)

9. If two trains of length a metres and b metres are moving in the

same direction atu m/s and v m/s, then:

The time taken by the faster train to cross the slower

train =

(a + b) sec.

(u - v)

10. If two trains (or bodies) start at the same time from points A

and B towards each other and after crossing they

take a and b sec in reaching B and A respectively, then:

(A's speed) : (B's speed) = (b : a)


http://www.indiabix.com/aptitude/time-and-distance/formulas

SumitShrivastava

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Example 1:-A train running at the speed of 60 km/hr crosses a pole

in 9 seconds. What is the length of the train?

Solution:-

Speed= ( 60 x 5

)m/sec = ( 50

)m/sec. 18 3

Length of the train = (Speed x Time).

Length of the train =

m = 150 m

Example 2:-A train 125 m long passes a man, running at 5 km/hr

in the same direction in which the train is going, in 10 seconds.

The speed of the train is:

Solution:-

Speed of the train relative to man =

125

m/sec 10

=

25

m/sec. 2

=

25 x

18

km/hr 2 5

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = (x - 5)

km/hr.

x - 5 = 45 x = 50 km/hr.

Example 3:-The length of the bridge, which a train 130 metres

long and travelling at 45 km/hr can cross in 30 seconds, is:

Solution:-

Speed =

45 x 5

m/sec =

25

m/sec. 18 2

Time = 30 sec.

Let the length of bridge be x metres.


SumitShrivastava

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Then, 130 + x

= 25

30 2

2(130 + x) = 750

x = 245 m.

Example 4:-Two trains running in opposite directions cross a man

standing on the platform in 27 seconds and 17 seconds

respectively and they cross each other in 23 seconds. The ratio of

their speeds is:

Solution: -Let the speeds of the two trains be x m/sec and y m/sec

respectively.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

27x + 17y = 23

x+ y

27x + 17y = 23x + 23y

4x = 6y

x =

3 .

y 2

Example 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 is 54 km/hr, what is the length of the platform?

Solution :-

Speed =

54 x 5

m/sec = 15 m/sec. 18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then, x + 300

= 15 36

x + 300 = 540

x = 240 m.

*****


SumitShrivastava

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Time & Work Formulae

Work from Days:If A can do a piece of work in n days, then

A's 1 day's work =

1 .

n

1. Days from Work:

If A's 1 day's work = 1 , Then A can finish the work in n days.

n

2. Ratio:

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

Example 1:-A can do a work in 15 days and B in 20 days. If

they work on it together for 4 days, then the fraction of the work

that is left is :

Solution:-

A's 1 day's work = 1

; 15

B's 1 day's work = 1

; 20

(A + B)'s 1 day's work =

1 +

1

= 7

. 15 20 60

(A + B)'s 4 day's work =

7 x 4

= 7

. 60 15

Therefore, Remaining work =

1 - 7

= 8

. 15 15

Example 2:-A can lay railway track between two given stations

in 16 days and B can do the same job in 12 days. With help of

C, they did the job in 4 days only. Then, C alone can do the job

in:


SumitShrivastava

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Solution:-

(A + B + C)'s 1 day's work = 1

, 4

A's 1 day's work = 1

, 16

B's 1 day's work = 1

. 12

C's 1 day's work = 1

-

1 +

1

=

1 -

7

= 5

. 4 16 12 4 48 48

So, C alone can do the work in 48

= 9 3

Days. 5 5

Example 3:-A, B and C can do a piece of work in 20, 30 and 60

days respectively. In how many days can A do the work if he is

assisted by B and C on every third day?

Solution;-

A's 2 day's work =

1 x 2

= 1

. 20 10

(A + B + C)'s 1 day's work =

1 +

1 +

1

= 6

= 1

. 20 30 60 60 10

Work done in 3 days =

1 +

1

= 1 .

10 10 5

Now, 1

Work is done in 3 days. 5

Whole work will be done in (3 x 5) = 15 days.

Example 4:- A is thrice as good as workman as B and therefore

is able to finish a job in 60 days less than B. Working together,

they can do it in:

Solution: -Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A

takes 1 day.


SumitShrivastava

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