A) 6%
B) 8%
C) 10%
D) 12%
Correct Answer: D
Solution :
Let the rate be r% per annum. Then, SI = Rs.\[\left( 500\times \frac{r}{100}\times 2 \right)=\,\,Rs.\,\,(100r)\] \[CI=Rs.\,\,\left[ 500\times {{\left( 1+\frac{r}{100} \right)}^{2}}-5000 \right]\] \[=Rs.\,\,\left\{ 5000\times \left[ {{\left( 1+\frac{r}{100} \right)}^{2}}-1 \right] \right\}\] \[=Rs.\,\,\left[ 5000\times \left( \frac{{{r}^{2}}}{10000}+\frac{r}{50} \right) \right]\] \[=Rs.\,\,\frac{5000({{r}^{2}}+200r)}{10000}=Rs.\,\,\left( \frac{{{r}^{2}}}{2}+100r \right)\]\[(CI)-(SI)=\left( \frac{{{r}^{2}}}{2}+100r \right)-(100r)=\frac{{{r}^{2}}}{2}\] \[\therefore \] \[\,\frac{{{r}^{2}}}{2}=72\Rightarrow {{r}^{2}}=144\] \[\Rightarrow \] \[r=\sqrt{144}=12\] Hence, rate = 12%
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