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

Let no. of people be x.

Each person receives = ₹ $\dfrac{6500}{x}$

According to question,

$\Rightarrow \dfrac{6500}{x + 15} = \dfrac{6500}{x} - 30 \\[1em] \Rightarrow \dfrac{6500}{x} - \dfrac{6500}{x + 15} = 30 \\[1em] \Rightarrow \dfrac{6500(x + 15) - 6500x}{x(x + 15)} = 30 \\[1em] \Rightarrow \dfrac{6500x + 97500 - 6500x}{x^2 + 15x} = 30 \\[1em] \Rightarrow 97500 = 30x^2 + 450x \\[1em] \Rightarrow x^2 + 15x = 3250 \\[1em] \Rightarrow x^2 + 15x - 3250 = 0 \\[1em] \Rightarrow x^2 + 65x - 50x - 3250 = 0 \\[1em] \Rightarrow x(x + 65) - 50(x + 65) = 0 \\[1em] \Rightarrow (x + 65)(x - 50) = 0 \\[1em] \Rightarrow x = -65, 50$

No. of people cannot be negative,

∴ x = 50.

Hence, no. of people = 50.