A) \[Rs.2,500\]
B) \[Rs.2,700\]
C) \[Rs.2,800\]
D) \[Rs.3000\]
Correct Answer: C
Solution :
Let the sum be Rs. P. Then, \[S.I.=\frac{P\times r\times t}{100}=\frac{P\times 5\times 2}{100}=\frac{P}{10}\] \[C.I.=P\,{{\left( 1+\frac{r}{100} \right)}^{n}}-P=P{{\left( 1+\frac{5}{100} \right)}^{2}}-P\] \[\therefore \,\,\,\,\,P{{\left( \frac{21}{20} \right)}^{2}}-P-\frac{P}{10}=7\] \[\frac{P\times 144-400P-40P}{400}=7\] \[P=7\times 400\Rightarrow P\,2800\] So, the sum \[=\,\,\underline{\mathbf{Rs}\mathbf{.}\,\mathbf{2800}}\] Shortcut: Using direct formula of Difference for 2 years \[=\frac{P\times {{r}^{2}}}{{{100}^{2}}}\,\,\,\Rightarrow \,\,\,\,7=\frac{P\times {{5}^{2}}}{{{100}^{2}}}\]
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