Question
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum (in Rs.) is:
Answer: Option A
$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{be}}\,Rs.\,x.\,{\text{Then}}, \cr
& {\text{C}}{\text{.I}}{\text{.}} = {x{{\left( {1 + \frac{4}{{100}}} \right)}^2} - x} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{{676}}{{625}}x - x} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{51}}{{625}}x \cr
& {\text{S}}{\text{.I}}{\text{.}} = {\frac{{x \times 4 \times 2}}{{100}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2x}}{{25}} \cr
& \therefore \frac{{51x}}{{625}} - \frac{{2x}}{{25}} = 1 \cr
& \Rightarrow x = 625 \cr} $$
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$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{be}}\,Rs.\,x.\,{\text{Then}}, \cr
& {\text{C}}{\text{.I}}{\text{.}} = {x{{\left( {1 + \frac{4}{{100}}} \right)}^2} - x} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{{676}}{{625}}x - x} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{51}}{{625}}x \cr
& {\text{S}}{\text{.I}}{\text{.}} = {\frac{{x \times 4 \times 2}}{{100}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2x}}{{25}} \cr
& \therefore \frac{{51x}}{{625}} - \frac{{2x}}{{25}} = 1 \cr
& \Rightarrow x = 625 \cr} $$
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