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

24

x months = \(\frac{x }{12 }\) years

Simple interest of x years = 1580 - 1500 = 80

By using formula ,

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

80  = \(\frac{1500 × x × x }{100 × 9 × 12 }\)

16  = \(\frac{ x × x }{  9 × 4 }\)

x × x = 576

x = 24