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# Ratio (Nishpatti) Shortcut Tricks for RRB & Competitive Exams

## 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,
Ex. 3 / 15 = 1 / 5
a and d called extremes, where as band c called mean terms.
Proportion of quantities
the four quantities a, b, c, d said proportion then we can express it
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, b2 = 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 = ?

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 = ?

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 = ?

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 = ?

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 = ?

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?

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 ?

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 :

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 :

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 ?

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.

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.

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.

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 :

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
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 :

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 ?

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 .