Question

Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.

Answer 1

Let the original number of persons be x.

Total money which was divided = Rs. 6500

Each person share = Rs. `6500/x`

From the given information

`6500/x - 6500/(x + 15) = 30`

`3250/(x(x + 15)) = 1`

x² + 15x – 3250 = 0

x² + 65x – 50x – 3250 = 0

x(x + 65)(x – 50) = 0

x = –65, 50

Since, the number of persons cannot be negative.

Hence, the original number of persons is 50.