Question
A man invests 40% of a certain amount at a simple
interest rate of 17% per annum, 60% of the remaining amount at a simple interest rate of 20% per annum, and the rest at a simple interest rate of 25% per annum. After how many years will the total interest earned from all the investments be equal to the initial sum invested? [Consider all the investments were made for the same time period]Solution
Let the total sum invested be Rs. '100x' So, sum invested at 17% p.a. = 100x X 0.4 = Rs. '40x' And sum invested at 20% p.a. = (100x - 40x) X 0.6 = Rs. '36x' And sum invested at 25% p.a. = (100x - 40x - 36x) = Rs. '24x' Simple interest = Sum X rate of interest X time period ÷ 100 So, total interest earned each year = {(40x X 17 X 1)/100} + {(36x X 20 X 1)/100} + {(24x X 25 X 1)/100} = 6.8x + 7.2x + 6x = Rs. '20x' So, required time = 100x ÷ 20x = 5 years
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