The compound interest on a sum of money for two years is Rs 52 and the simple interest for two years at the same rate is Rs 50. Then the rate of interest is

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10%

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Solution

The correct option is B 8%
Given,
Simple Interest for two years is 50
$\frac{P \times T \times R}{100} = S i m p l e I n t e r e s t$
$\frac{P \times 2 \times R}{100} = 50$
$P R = 2500$
$P = \frac{2500}{R}$ ................EQ(1)
Compound Interest for two years will be 52
$P {(1 + \frac{r}{100})}^{2} - P = 52$
$\Rightarrow P (1 + \frac{2 R}{100} + \frac{R^{2}}{10000} - 1) = 52$
$\Rightarrow P (\frac{2 R}{100} + \frac{R^{2}}{10000}) = 52$
$\Rightarrow P (\frac{200 R + R^{2}}{10000}) = 52$
$\Rightarrow P (\frac{200 R + R^{2}}{10000}) = 52$
$\Rightarrow P (200 R + R^{2}) = 520000$
$\Rightarrow 200 R + R^{2} = \frac{520000}{P}$
$\Rightarrow 200 R + R^{2} = 520000 \times \frac{R}{2500}$ (TAKING EQUATION FROM SIMPLE INTEREST EQ(1))
$\Rightarrow 200 R + R^{2} = 208 R$
$\Rightarrow R^{2} = (208 R - 200 R)$
$\Rightarrow R^{2} = 8 R$
$R = 8$
Rate will be 8%

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The compound interest on a sum of money for two years is Rs 52 and the simple interest for two years at the same rate is Rs 50. Then the rate of interest is

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