The ratio of Boys and Girls in a group is 7 : 6. If 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls becomes 4 : 3. What is the total number of boys and girls initially in the group?

A. 78

B. 104

C. 117

D. 91

SSC CGL 2019 Tier - 1 4 March 2020 Shift 2

Solution:

Let the number of boys and number of girls initially be x and y respectively.

It is given that,

x/y = 7/6

6x - 7y = 0 ............(1)

If 4 more boys join the group and 3 girls leave the group

Number of boys in the group = x + 4

Number of girls in the group = y - 3

New ratio is (x + 4)/(y - 3) = 4/3

3x + 12 = 4y - 12

3x - 4y = -24 ............(2)

Multiply equation 2 by 2 and subtract from equation 1, we get

y = 48

Put y = 48 in eq 1, we get,

6x - 7 * 48 = 0

x = 56

The number of boys and girls initially in the group = x + y = 48 + 56

= 104

Hence, (B) is the correct answer.

This question is based on the topic of Ratio and Proportion.


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