Rs. 9000 were divided equally among a certain number of persons. Had t

1.	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» Let the original number of people be ‘a’. Given, 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= 9000/a \(\Rightarrow \frac{9000}{a\,+\,20}=\frac{9000}{a}-160\) ⇒ 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

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»

Let the original number of people be ‘a’.

Given, 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= 9000/a

\(\Rightarrow \frac{9000}{a\,+\,20}=\frac{9000}{a}-160\)

⇒ 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