A sum of Rs. 1500 is invested at simple interest for x months. If the rate of interest is $$\left(\frac{x}{9}\right)$$% per annum, then the sum grows to Rs. 1580. What is the value of x ?

A sum of Rs. 1500 is invested at simple interest for x months. If the rate of interest is $$\left(\frac{x}{9}\right)$$% per annum, then the sum grows to Rs. 1580.

simple interest = 1580-1500 = Rs. 80

simple interest = $$\frac{\left(P\times R\times\ T\right)}{100}$$

80 = $$\frac{\left(1500\times\left(\frac{x}{9}\right)\times\ \left(\frac{x}{12}\right)\right)}{100}$$

$$80=\left(5\times\left(\frac{x}{3}\right)\times\ \left(\frac{x}{12}\right)\right)$$

$$x^2\ =\ 576$$
x = 24