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