Question
On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to Rs. 63 ?
Answer: Option C
$$\eqalign{
& {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr
& {\text{Time = 2 year}} \cr
& {\text{Accroding to question,}} \cr
& \Rightarrow P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right] - \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left( {\frac{{11025 - 10000}}{{10000}}} \right) - \frac{{10P}}{{100}} = 63 \cr
& \Rightarrow \frac{{1025P}}{{10000}} - \frac{{10P}}{{100}} = 63 \cr
& \Rightarrow \frac{{1025P - 1000P}}{{10000}} = 63 \cr
& \Rightarrow 25P = Rs.630000 \cr
& \Rightarrow P = \frac{{630000}}{{25}} \cr
& \Rightarrow P = Rs. 25200 \cr
& {\text{Hence}},\,{\text{sum Rs}}{\text{. 25200}} \cr} $$
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$$\eqalign{
& {\text{Rate of interest = 5}}\% {\text{ per annum}} \cr
& {\text{Time = 2 year}} \cr
& {\text{Accroding to question,}} \cr
& \Rightarrow P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right] - \frac{{P \times r \times t}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{P \times 5 \times 2}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left[ {{{\left( {\frac{{105}}{{100}}} \right)}^2} - 1} \right] - \frac{{10P}}{{100}}{\text{ = 63}} \cr
& \Rightarrow P\left( {\frac{{11025 - 10000}}{{10000}}} \right) - \frac{{10P}}{{100}} = 63 \cr
& \Rightarrow \frac{{1025P}}{{10000}} - \frac{{10P}}{{100}} = 63 \cr
& \Rightarrow \frac{{1025P - 1000P}}{{10000}} = 63 \cr
& \Rightarrow 25P = Rs.630000 \cr
& \Rightarrow P = \frac{{630000}}{{25}} \cr
& \Rightarrow P = Rs. 25200 \cr
& {\text{Hence}},\,{\text{sum Rs}}{\text{. 25200}} \cr} $$
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