__Ratio (Nishpatti) Shortcut Tricks for RRB&Competitive Exams__

Ratio and proportion is a very general topic for all bank exams. Mostly bank exams includes this topic in quantitative section.

Ratio is a quantity which represents the relationship between two similar quantities. It expresses a magnitude by which quantity is multiple of another one. Ratio is represented as 2:3 or 2/3. Here, numerator i.e. 2 is known as

**“ANTECEDENT”**and denominator i.e. 3 is known as**“CONSEQUENT”**.If antecedent is more than the consequent, then it is known as improper ratio and if less ,then it is known as proper ratio.

__What is Ratio__A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b In ratio a : b , we can say that a as the

**first term**or**antecedent**and b, the**second term**or**consequent**.**Example :**The ratio 4 : 9 we can represent as 4 / 9 after this 4 is a antecedent and , consequent = 9

**What is Proportion?**The idea of proportions is that two ratio are equal.

If a : b = c : d, we write a : b : : c : d,

If a : b = c : d, we write a : b : : c : d,

**Ex.**3 / 15 = 1 / 5**a**and**d**called**extremes,**where as**b**and**c**called**mean terms**.

**Proportion of quantities**the four quantities a, b, c, d said proportion then we can express it

Then

**a : b = c : d**Then

**a : b : : c : d <–> ( a x d ) = ( b x c )****product of means = product of extremes.**If there is given three quantities like

**a, b, c**of same kind then then we can say it proportion of continued.**a : b = b : c**the**middle number**b is called**mean proportion.****a**and**c**are called**extreme numbers.****So, b**^{2}**=****ac****. ( middle number )**^{2}**= ( First number x Last number ).**## Ratio Example 1

**Example 1: **If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ?

**Answer :**

P : Q : R = 2 : 3 : 4 . Let P = 2k, Q = 3k, R = 4k. Then,

P / Q = 2k / 3k = 2 / 3 , Q / R = 3k / 4k = 3 / 4 and R / P = 4k / 2k = 2 / 1.

SO, P / Q : Q / R : R / P = 2 / 3 : 3 / 4 : 2 / 1 =

**8 : 9 : 24 .**

**Example 2: **If P : Q = 2 : 3 and Q : R = 4 : 5 , then R : P = ?

**Answer :**

P / R = ( P / Q x Q / R ) = ( 2 / 3 x 4 / 5 ) = 8 / 15

=R / P = 15 / 8 = R : P = 15 : 8.

**Example 3: **If 2P = 3Q = 4R, Then P : Q : R = ?

**Answer :**

Let 2P = 3Q = 4R = k , Then , P = k / 2, Q = k / 3 , R = k / 4.

SO , P : Q : R = k / 2 : k / 3 : k / 4 = 2 : 3 : 4

**Example 4: **If a : b = 3 : 7 and b : c = 5 : 9, find a : b : c .

**Answer:**A : B = 3 : 7, B : C = 5 : 9

= ( 5 x 7 / 5 ) : ( 9 x 7 / 5 ) = 7 : 63 / 5 .

= A : B : C = 3 : 7 : 63 / 5 = 15 : 35 : 63 .

**Example 5: **If P : Q = 2 : 3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ?

**Answer :**

P / S = ( P / Q x Q / R x R / S ) = ( 2 /3 x 4 / 5 x 6 / 7 ) = 16 / 35 = P : S = 16 : 35 .

**Example 6: **If P : Q = 1 / 2 : 3 /8 , Q : R = 1 / 3 : 5 / 9 and R : S = 5 / 6 : 3 / 4 , Then P : Q : R : S = ?

**Answer :**

P : Q = 1 / 2 : 3 / 8 = 4 : 3 , Q : R = 1 / 3 : 5 / 9 = 3 : 5 and R : S = 5 / 6 : 3 / 4 = 10 : 9

P : Q = 4 : 3 , Q : R = 3 : 5 , R : S = 10 / 2 : 9 / 2 = 5 : 9 / 2

P : Q : R : S = 4 : 3 : 5 : 9 / 2 = 8 : 6 : 10 : 9 .

**Example 7:**Rama distributes his pencil among his four friends Rakesh, Rahul, Ranjan, and Rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . What is the minimum number of pencils that the person should have?

**Answer :**

Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5

**Step 1:**At First we need to do is LCM of 2,3,4 and 5 is 60.

**Step 2:**Then pencil are distributed in ratio among friends,

Rakesh = ( 1 / 2 x 60 ) = 30.

Rahul = ( 1 / 3 x 60 ) = 20.

Ranjan = ( 1 / 4 x 60 ) = 15.

Rohit = ( 1 / 5 x 60 ) = 12.

**Step 3:**Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.

For minimum number of pencils x = 1 .

**The person should have atleast 77 pencils.**

**Example 8:**Two numbers are respectively 40% and 60% more than third number.Findthe ration of two numbers ?

**Answer :**

**Step 1:**Let the third number is A

Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B / 5.

**Step 2:**now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.

**Example 9:**If 75 is divided into three parts proportional to 3, 5, 8, 9 then the smallest part is :

**Answer :**

ratio is = 3 : 5 : 8 : 9, sum of ratio terms is = 25.

So the smallest part is = ( 75 x 3 / 25 ) = 9 .

**Example 10: **If A : B = 4 : 9 and B : C = 3 : 6 , then A : C is :

**Answer :**(A / B = 4 / 9, B / C = 3 / 6 )

= A / C = ( A /B x B / C) = ( 4 / 9 x 3 / 6 ) = 2 / 9 = A : C = 2 : 9.

## Ratio Example 2

**Example 1 :**On dividing a sum of Rs 832 between Paul and john in the ratio 1 / 3 : 1 / 5 , their shares are :

**Answer :**

So the given ratio is = 1 / 3 : 1 / 5 = 5 : 3

So , the 1st part = Rs ( 832 x 5 / 8 ) = Rs 520 , 2nd part = Rs ( 832 x 3 / 8 ) = Rs 312

**So , their shares are : 520 and 312 .**

**Example 2 :**The Salary of Three friend A, B, C are divided into ratio 5 : 6 : 8.If the increment has given of 10%, 20%, 25%, Find the new ratio of three friend salary ?

**Answer :**

**Step 1:**We assume ration as 5x, 6x, 8x

now the increment of new salary is A = 110 / 100, B = 120 / 100, C = 125 / 100.

**Step 2:**A,s new salary is 110 X 5x / 100 = 55x / 10.

B,s new salary is 120 X 6x / 100 = 36x / 5.

C,s new salary is 125 X 8x / 100 = 10.

**Step 3:**New ratio is 55x / 10 : 36x / 5 : 10.

**Example 3 :**Share Rs.4200 among joy, sanjay and bijoy in the ration 2 : 4 : 6.Find the amount received by sanjay.

**Answer :**

Amount received by sanjay.

4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount

**So, the Amount received by sanjay is 1400.**

**Example 4 :**Rs 1210 were divided among three person P, Q, R so that P : Q = 5 : 4 and Q : R = 9 : 10. Then R gets the amount.

**Answer :**

P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.

So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40

Sum of ratio terms is = ( 45 + 36 + 40 ) =121.**R share of amount is Rs (1210 x 40 / 121) = Rs. 400 .**

**Example 5 :**Find the mean proportional between given two number that is 64 and 49.

**Answer :**

The mean proportion of two numbers is

Root of 64 and 49 is √8 x √ 7 = 8 x 7 = 56.

**So, the mean proportional is 56.**

**Example 6 :**Rs 64000 are divided among three friends in the ratio 3 / 5 : 2 / 1 : 5 / 3 . The share of the second friend is :

**Answer :**

Here the given ratio is = 3 / 5 : 2 / 1 : 5 / 3 = 9 : 30 : 50 .

**So the Share of the second friend = Rs ( 64000 x 30 / 64) = 30000 .**

**Example 7 :**Which of the following ratio is the greatest ?

7 : 15 , 15 : 23 , 17 : 25 , 21 : 29

7 / 15 = 0.466

15 / 23 = 0.652

17 / 25 = 0.68

21 / 29 = 0.724

**Answer :**7 / 15 = 0.466

15 / 23 = 0.652

17 / 25 = 0.68

21 / 29 = 0.724

**So, 0.724 is greatest and therefore, 21 : 29 .****Example 8 :**What number has to be added to each term of 3 : 5 to make the ratio 5 : 6 :

**Answer :**

Let the number to be added x , Then

3 + x / 5 + x = 5 / 6

6 ( 3 + x ) = 5 ( 5 + x )

x = ( 25 – 18 ) = 7

**So , the number to be added is 7 .**

**Example 9 :**Rs. 385 were divided among P , Q , R in such a way that P had Rs 20 more than Q and R had Rs 15 more than P . How much was R’s share ?

**Answer :**

Let Q gets Rs x. Then We can say P gets Rs (x + 20 ) and R gets Rs ( x + 35) .

x + 20 + x + x + 35 = 385

3x = 330

x = 110 .

**R’s share = Rs ( 110 + 35 ) = Rs 145 .**

**Example 10 :**A certain amount was divided between A and B in the ratio 4 : 3 . If B’s share was Rs, 4800, the total amount was ?

**Answer :**

If B ‘s share is Rs, 3, total amount = Rs, 7

**If B’s share is Rs, 4800, total amount = Rs, (7 / 3 x 4800) = 1120 .**

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