Question

Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

Answer 1

Let’s consider the original number of people as ‘a’.

Given that, Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less.

Amount which each receives when a persons are present = \(\frac{9000}{a}\)

Expressing the given condition we have,

⇒ 9000a = (9000 – 160a)(a + 20)

⇒ 9000a = 9000a + 180000 – 160a² – 3200a

⇒ a² + 20a – 1125 = 0

⇒ a² + 45a – 25a – 1125 = 0

⇒ a(a + 45) – 25(a + 45) = 0

⇒ (a – 25)(a + 45) = 0

⇒ a = 25 or a = -45 (neglected as the number of people can never be negative)

Therefore, the original number of people = 25.