₹ 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. 45
B. 50
C. 55
D. 48

Answer

B

Explanation

Let the original number of persons = x
According to the question
`(6500)/x = (6500)/((x + 15)) + 30 `
or `6500/x = (6500 + 30(x + 15))/((x + 15))`
or `6500/x = (6500 + 30x + 450)/((x + 15))`
or `6500(x + 15) = x(6500 + 30x + 450)`
or, `6500x + 97500 = 6500x + 30x^2 + 450x`
or, `30x^2 + 450x - 97500 = 0 `
or, `x^2 + 15x - 3250 = 0 `
or, `x^2 +65x -50x - 3250 = 0 `
or, `x(x + 65) - 50(x +65) = 0 `
or, `(x + 65) (x - 50) = 0 `
or, `x=-65 and x = 50 `
But, x =-65 is rejected.
[`because` No. of persons can.t be negative]
Therefore, the original number of persons = 50.