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The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is ?

a) Rs. 1550
b) Rs. 1650
c) Rs. 1750
d) Rs. 2000

Answer: c
Explanation:
$$\eqalign{ & {\text{C}}{\text{.I}}{\text{.}} {\text{ = Rs}}{\text{.}}\left[ {4000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^2} – 4000} \right] \cr & = {\text{ Rs}}{\text{.}}\left( {4000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} – 4000} \right) \cr & = {\text{Rs}}{\text{. 840}} \cr & {\text{Sum = Rs}}{\text{.}}\left( {\frac{{420 \times 100}}{{3 \times 8}}} \right) \cr & = {\text{Rs}}{\text{. }}1750 \cr} $$

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