Question

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

Answer 1

Let the original number of children be $$n$$.

Original share of each child $$= ₹\ \frac{7500}{n}$$.

If 20 children are less, share of each child $$= ₹\ \frac{7500}{n - 20}$$.

Given: $$\frac{7500}{n - 20} - \frac{7500}{n} = 100$$ 

Dividing by 100: $$\frac{75}{n - 20} - \frac{75}{n} = 1$$

$$75\left(\frac{n - (n - 20)}{n(n - 20)}\right) = 1$$

$$\frac{1500}{n^2 - 20n} = 1$$

$$n^2 - 20n - 1500 = 0$$ 

Factoring: $$(n - 50)(n + 30) = 0$$

Since number of children cannot be negative, $$n = 50$$.

Hence, the original number of children is 50.