Rs. ‘y’ was invested in scheme A at the rate of 21% per annum for (t+2) years. Rs. (y+2400) was invested in scheme B at the rate of 18% per annum for ‘t’ years. The interest obtained from both of the schemes together is Rs. 14484. If Rs. (y-200) was invested in scheme C at the rate of 25% per annum on compound interest compounded annually, then after two years Rs. 2812.5 will be obtained as an interest. Find out the value of ‘t’.

Solution

If Rs. (y-200) was invested in scheme C at the rate of 25% per annum on compound interest compounded annually, then after two years Rs. 2812.5 will be obtained as an interest. (y-200) of (100+25)% of (100+25)% - (y-200) = 2812.5 (y-200) of 125% of 125% - (y-200) = 2812.5 (y-200)[1.5625-1] = 2812.5 0.5625x(y-200) = 2812.5 (y-200) = 5000 y = 5000+200 = 5200 Rs. ‘y’ was invested in scheme A at the rate of 21% per annum for (t+2) years. Rs. (y+2400) was invested in scheme B at the rate of 18% per annum for ‘t’ years. The interest obtained from both of the schemes together is Rs. 14484. y x 21% x (t+2) + (y+2400) x 18% x t = 14484 Put the value of ‘y’ in the above equation. 5200 x 21% x (t+2) + (5200+2400) x 18% x t = 14484 5200 x 21% x (t+2) + 7600 x 18% x t = 14484 1092 x (t+2) + 1368 x t = 14484 1092t+2184 + 1368t = 14484 2460t = 14484-2184 2460t = 12300 Value of ‘t’ = 5