Question 101

In a college, the ratio of boys to girls is 31 : 23 respectively. When 75 more girls join the college, this ratio becomes 124 : 107. How many more girls should join the college to make the number of boys and girls equal?

Solution

Let the number of boys initially = $$31x$$

=> Number of girls = $$23x$$

Acc to ques,

=> $$\frac{31x}{23x + 75} = \frac{124}{107}$$

=> $$3317x = 2852x + 9300$$

=> $$3317x - 2852x = 465x = 9300$$

=> $$x = \frac{9300}{465} = 20$$

=> Number of boys = $$31 \times 20 = 620$$

Number of girls = $$23 \times 20 + 75 = 535$$

$$\therefore$$ Number of girls who should join the college to make number of boys and girls equal

= $$620 - 535 = 85$$

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