Question

Sangram invests certain sum for 2 years in scheme P offering compound interest of 20% per annum. He also invests less than previous by Rs. 1600 in scheme Q for 3 years offering simple interest at 10% per annum. The interest received from scheme P was twice the interest received from scheme Q. what is the sum of money invested by Sangram in scheme Q?​

Answer 1

Let the certain amount invested in the scheme P be x in Rs. So that x is invested for 2 years offering compound interest of 20% annually.

Thus in scheme Q Sangram invests Rs. (x - 1600) in the scheme Q for 3 years offering simple interest of 10% annually.

The total interest received from the scheme P is,

x · (120 / 100)² - x = (36x / 25) - x = 11x / 25

And the total interest received from the scheme Q is,

(x - 1600) · (10 / 100) · 3 = 3(x - 1600) / 10.

Given that the interest received from P is twice that received from Q, i.e.,

11x / 25 = 6(x - 1600) / 10

11x / 25 = 15(x - 1600) / 25

11x = 15(x - 1600)

11x = 15x - 24000

4x = 24000

x = Rs. 6000