#### 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.

#### Solution

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`

`x^2 + 15x - 3250 = 0`

`x^2 + 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 s of person is 50

Is there an error in this question or solution?

Solution 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. Concept: Quadratic Equations.