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6.Interest
medium
On a sum of money, the simple interest for $2$ $years$ is ₹ $660$, while the compound interest is ₹ $696.30$, the rate of interest being the same in both the cases. The rate of interest (In $\%$) is
A
$10$
B
$10.5$
C
$12$
D
$11$
Solution
Let the rate of interest be $R \%$.
$\begin{array}{l}\text { S.I. }=\frac{P \times 2 \times R}{100}=660 \\\text { C.I. }=P\left[\left(1+\frac{R}{100}\right)^{2}-1\right]=696.30\end{array}$
$\frac{(2)}{(1)} \Rightarrow \frac{\left[\left(1+\frac{R}{100}\right)^{2}-1\right]}{\frac{2 R}{100}}=\frac{696.30}{660}$
$\Rightarrow \quad \frac{100}{2 R}\left(\frac{R^{2}}{100^{2}}+\frac{2 R}{100}\right)=1.055$
$\begin{array}{ll}\Rightarrow & \frac{R}{200}+1=1.055 \\\text { or } & R=(1.055-1) \times 200=11 \%\end{array}$
Standard 13
Quantitative Aptitude
