Question
The difference between compound and simple interest on a certain sum for 3 years at 5% per annum is Rs. 122. The sum is = ?
Answer: Option A
$$\eqalign{
& \Rightarrow P\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1 - \frac{3}{{20}}} \right] = 122 \cr
& \Rightarrow P\left[ {\frac{{{{21}^3} - {{20}^3} - 3 \times {{20}^2}}}{{{{20}^3}}}} \right] = 122 \cr
& \Rightarrow P\left[ {\frac{{9261 - 8000 - 1200}}{{8000}}} \right] = 122 \cr
& \Rightarrow P \times \frac{{61}}{{8000}} = 122 \cr
& \Rightarrow P = \frac{{8000 \times 122}}{{61}} \cr
& \Rightarrow P = {\text{Rs}}{\text{.}}\,16000 \cr} $$
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$$\eqalign{
& \Rightarrow P\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1 - \frac{3}{{20}}} \right] = 122 \cr
& \Rightarrow P\left[ {\frac{{{{21}^3} - {{20}^3} - 3 \times {{20}^2}}}{{{{20}^3}}}} \right] = 122 \cr
& \Rightarrow P\left[ {\frac{{9261 - 8000 - 1200}}{{8000}}} \right] = 122 \cr
& \Rightarrow P \times \frac{{61}}{{8000}} = 122 \cr
& \Rightarrow P = \frac{{8000 \times 122}}{{61}} \cr
& \Rightarrow P = {\text{Rs}}{\text{.}}\,16000 \cr} $$
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