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 the original number of persons be x.
Then, by the given information,

`9000/x-160=900/(x+20)`

`(9000-160x)/x=9000/(x+20)`

(x + 20)(9000 - 160x) = 9000x

9000x - 160x² + 180000 - 3200x = 9000x

160x2 - 180000 + 3200x = 0

x² - 1125 + 20x = 0

x² - 1125 + 20x + 100 = 100

(x + 10)² = 1225

x + 10 = 35

x = 35 - 10

x = 25

Thus, the original number of persons is Rs 25.