Question 60

The ratio of boys and girls in a groupis 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. Whatis the total number of boys and girls initially in the group?

Solution

The ratio of boys and girls in a group is 7 : 6.

Let the boys be 7x and girls be 6x.

When 4 more boys join the group and 3 girls leave the group, then the ratio of boys to girls = 4 : 3

$$\frac{7x + 4}{6x -3} = \frac{4}{3}$$

21x + 12 = 24x -12

3x = 24

x = 8

Initially boys and girls = 7x + 6x = 13x = 13 $$\times$$ 8 = 104

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