₹ 6,500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got ₹ 30 less. Find the original number of persons?

Options

A. a. 40
B. b. 45
C. c. 50
D. d. 55

Answer

C

Explanation

Let the original number of persons be x
`therefore (6500)/(x) - (6500)/(x + 15) = 30`
`therefore (6500 (x + 15-x))/(x(x + 15)) = 30`
`therefore 6500 xx 15 = 30(x^2 + 15x)`
`30x^2 + 450x = 9750`
`3x^2-150x + 195x - 9750 = 0`
`3x(x-50)+195(x-50) = 0`
`therefore x = 50`