In a school, the number of boys and girls were in the ratio 5 : 7 . Eight more boys were admitted during the session. The new ratio of girls and boys is 1 : 1. In the beginning the difference between the number of boys and that of girls was:

Correct option is D

Given:

The number of boys and girls were in the ratio =5 : 7

After adding 8 boys new ratio =1:1

Solution:

Let the number of boys in the beginning = 5x

The number of girls =7x .

After 8 more boys were admitted, the new number of boys becomes 5x + 8 .
It is given that the new ratio of girls to boys is 1:1, so we have the equation:

7x = 5x + 8
7x - 5x = 8
2x = 8
x = 4
Thus, the initial number of boys was 5x = 20 and the initial number of girls was 7x = 28 .

The difference between the number of boys and girls in the beginning was:

28 - 20 = 8 .