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 ma…

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
= $620 - 535 = 85$