Quantitative Aptitude: Ratios- Concepts & Problems

This article explains all concepts related to Ratios & questions asked in Bank & other exams.

Ratios

When we talk of ratios, we are essentially commenting on the ‘relative’ amounts. 

E.g. If the ratio of boys and girls in a class is 4 : 3 and the total number of students in the class is 84, find the number of boys and girls.

Assuming the number of boys and girls to be 4k and 3k, we have 4k + 3k = 84 i.e. k = 12

Thus the number of boys and girls is 48 and 36 respectively.

Simple haan!

Dividing a given sum in a ratio

E.g. Divide Rs. 72 in the ratio 2 : 3 : 4.

Let the three parts be 2k, 3k and 4k respectively. The total of the three parts will be the total amount i.e. Rs. 72

Thus, 2k + 3k + 4k = 72 i.e. 9k = 72 i.e. k = 8

Thus the three parts will be 2 × 8 = 16; 3 × 8 = 24; and 4 × 8 = 32

When Ratios are in Fractions

A, B and C’s shares are in the ratio 1:  1:  1

                                                          2   3   4

We multiply with the LCM of denominators to get rid of the fractions. Thus, A, B and C’s share are in ratio 6 : 4 : 3

Given a : b and b : c, finding a : c

E.g. If a : b is 3 : 4 and b : c is 5 : 6, find the ratio a : b : c.

Since b is common to the two ratios, we should make the numeric value of b the same in both the ratios.

REMEMBER: When all terms of a ratio are multiplied with the same constant, 

the ratio does not change.

Thus in the first ratio b could be changed to any multiple of 4 and in the second ratio b could be 

changed to any multiple of 5. So, we should make b a multiple of 4 and 5 i.e. 20

• a : b is 3 × 5 : 4 × 5 i.e. 15 : 20
• b : c is 5 × 4 : 6 × 4 i.e. 20 : 24                

Thus, when b is 20, a is 15 and c is 24 and required ratio of a : b : c is 15 : 20 : 24.

A typical example

E.g. A bag has Re. 1, 50 paisa and 25 paisa coins. If the ratio of the number of coins of the respective denominations is 3 : 2 : 8 and the bag has a total amount of Rs. 156, find the number of 50 paise coins. 

Since the ratio is given of the number of coins, let the number of coins be 3k, 2k and 8k.

Remember these are the number of coins and equating 3k + 2k + 8k = 156 WILL BE WRONG since it is the total amount, not the number of coins.

The left hand side of this equation is the total number of coins and the right hand side, 156, is 

NOT the total number of coins but is the value of the number of coins. 

Thus, the number of coins will have to be transferred to value of coins, in Rs.

3k Re.1 coins will amount to 3k × 1 = Rs. 3k

2k 50-paise coins will amount to 2k × 0.5 = Rs. k

8k 25-paise  coins will amount to 8k × 0.25 = Rs. 2k.

Thus, total amount in bag will be 3k + k + 2k i.e. 6k and this will be equal to Rs. 156. 

Thus, 6k = 156 i.e. k = 26

We want to find the number of 50-paise coins and the required answer will be 2k i.e. 2 × 26 = 52 coins.

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