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The difference between compound and simple interest on a certain sum for 3 years at 5% per annum is Rs. 122. The sum is = ?

a) Rs. 16000
b) Rs. 15000
c) Rs. 12000
d) Rs. 10000

Answer: a
Explanation:
$$\eqalign{ & P\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} – 1 – \frac{3}{{20}}} \right] = 122 \cr & P\left[ {\frac{{{{21}^3} – {{20}^3} – 3 \times {{20}^2}}}{{{{20}^3}}}} \right] = 122 \cr & P\left[ {\frac{{9261 – 8000 – 1200}}{{8000}}} \right] = 122 \cr & P \times \frac{{61}}{{8000}} = 122 \cr & P = \frac{{8000 \times 122}}{{61}} \cr & P = {\text{Rs}}{\text{.}}\,16000 \cr} $$

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