Question
Person 'P' invested ₹4y at a simple interest rate of
35% per annum and ₹3y at a compound interest rate of 20% per annum (compounded annually), both for a duration of 2 years. The simple interest earned exceeds the compound interest by ₹3,700. Determine the total amount invested by 'P'.Solution
Simple interest = (Principal X time X rate) ÷ 100 = (4y X 2 X 35) ÷ 100 = Rs. '2.8y' CI = P X (1 + r/100)t - 1) , where 'P' is the sum invested, 'R' is the annual rate of interest and 'T' is the time period. CI = 3y X (1 + 20/100)2 - 1) Or, CI = 3y X [(1 + 0.2) 2 - 1] Or, CI =3y X [(1.2) 2 - 1] So, CI = 3y X 0.44 = Rs. '1.32y' ATQ, 2.8y - 1.32y = 3,700 Or, 1.48y = 3,700 So, 'y' = 2,500 Therefore, total sum invested by 'P' = 3y + 4y = 7y = 7 X 2,500 = Rs. 17,500
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