₹7500 were divided equally among a certain number of children

₹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

Let the original number of children be x.
each one gets 7500/𝑥                                                                                                                                                                When 20 children less, each would get 7500/𝑥-20
7500/𝑥 - 20 - 7500/𝑥 = 100
⇒ 𝑥² - 20𝑥 - 1500 = 0
⇒ (𝑥 - 50)(𝑥 + 30) = 0
∴ 𝑥 = 50