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6.Interest
hard
The compound interest on a certain sum for $2$ years at $10 \%$ per annum is ₹ $525 .$ The simple interest (In ₹) on the same sum for double the time at half the rate percent per annum is
A
$520$
B
$550$
C
$500$
D
$515$
Solution
(c) Let the Sum $=₹ 100 x$
For compound interest, $r =10 \%, t =2$ years.
$\begin{aligned} C.I &= P \left[\left(1+\frac{ r }{100}\right)^{ t }-1\right] \\ \Rightarrow & 100 x \left[\left(1+\frac{10}{100}\right)^{2}-1\right]=525 \\ & \Rightarrow 100 x \left[\left(\frac{11}{10}\right)^{2}-1\right]=525 \\ &=21 x =525 \\ x &=25 \end{aligned}$
Sum Invested $=₹ 2500$.
For S.I, $r=5 \%, 5=4$ years
$\begin{array}{ll}\text { S.I } & =\frac{\text { PNR }}{100} \\ & =\frac{2500 \times 5 \times 4}{100} \\ \text { S.I } & =\text { Rs. } 500\end{array}$
Standard 13
Quantitative Aptitude
