Question

Rs. $7500$ were divided equally among a certain number of children. Had there been $20$ less children, each would have received Rs. $100$ more. Find the original number of children.

Answer 1

Let the total number of children be $N$.

Now, each child gets Rs. $\frac{7500}{N}$

If there were 20 children less, each child gets Rs. $\frac{7500}{N-20}$

According to given condition,

$\frac{7500}{N-20}=\frac{7500}{N}+100$

$\therefore 7500N=7500(N-20)+100N(N-20)$

$\therefore 75N=75(N-20)+N(N-20)$

$\therefore 75N=75N-1500+N^2-20N$

$\therefore N^2-20N-1500=0$

$\therefore (N-50)(N+30)=0$

$\therefore N=50$ or $N=-30$

But, number of children cannot be negative hence, $N=50$

The original number of children is $50$.