Question : A borrows an amount of INR 3,600 from B at a rate of 20% simple interest for 2 years and lends 75% of this amount to C at 20% compound interest for 2 years. A uses the remaining amount for his purpose. Find the total loss incurred by A.
Option 1: INR 928
Option 2: INR 852
Option 3: INR 1,152
Option 4: INR 1,024
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Correct Answer: INR 1,152
Solution : Given, Principal borrowed by A from B = INR 3,600 Rate of interest charged by B on loan = 20% per year (simple interest) Time for which A borrowed from B = 2 years A lent 75% of the borrowed amount to C at a rate of 20% per year (compound interest) for 2 years We know, Simple Interest (SI) = $\frac{P × R × T}{100}$ Compound Interest (CI) = $P × [ (1 + \frac{R}{100})^T- 1 ]$ Total interest = CI - SI Where, P = principal amount, R = rate of interest per annum, and T = time in years Interest paid by A = Simple interest on loan from B = $\frac{P × R × T}{100}$ = $\frac{3600 × 20 × 2}{100}$ = IINR 1,440 Amount lent to C = 75% of INR 3,600 = INR 2,700 Interest received by A = Compound interest on the amount lent to C = $P × [ (1 + \frac{R}{100})^T- 1 ]$ = $2700 × [ (1 + \frac{20}{100})^2 - 1 ]$ = $2700 × \frac{11}{25}$ = INR 1188 Total loss incurred By A = 1440 - 1188 + amount for his Purpose. = 1440 - 1188 + 25% of 3600 = 1440 - 1188 + 900 = INR 1152 Hence, the correct answer is INR 1,152.
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