Question

In a class of $60$ students, each boy contributed rupees equal to the number of girls and each girl contributed rupees to the number of boys. If the total money then collected was $RS1600$. How many boys were there in the class?

Answer 1

$\Rightarrow$ Let boys be $x$, then girls be $60-x$

$\Rightarrow$ Contribution by boys $=x(60-x)$

$\Rightarrow$ Contribution by girls $=(60-x)x$

$\Rightarrow$ Total money collected $=Rs.1600$

$\therefore$ $60x-x^2+60x-x^2=1600$

$\Rightarrow$ $-2x^2+120x-1600=0$

$\Rightarrow$ $-2(x^2-60x+800)=0$

$\Rightarrow$ $x^2-60x+800=0$

$\Rightarrow$ $x^2-40x-20x+800=0$

$\Rightarrow$ $x(x-40)-20(x-40)=0$

$\Rightarrow$ $(x-40)(x-20)=0$

$\therefore$ $x=40$ and $x=20$

$\therefore$ Number of boys in class are $20$ or $40$