Answer : Option C

Explanation :

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Solution 1
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Let the rate of interest per annum be R%
$MF#%\begin{align}&\text{Amount after 2 years on Rs.15000 when interest is compounded annually }\\\\ &= \text{P}\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} = 15000\left(1 + \dfrac{\text{R}}{100}\right)^2\\\\&\text{Compound Interest =}15000\left(1 + \dfrac{\text{R}}{100}\right)^2 - 15000
= 15000\left[\left(1 + \dfrac{\text{R}}{100}\right)^2 - 1\right]\\\\ &\text{Simple Interest = }\dfrac{\text{PRT}}{100} = \dfrac{15000 \times \text{R} \times 2}{100} = \text{300R}\end{align}$MF#%
Difference between compound interest and simple interest = Rs.96
$MF#%\begin{align}&15000\left[\left(1 + \dfrac{\text{R}}{100}\right)^2 - 1\right] - \text{300R} = 96\\\\ &15000\left[1 + \dfrac{\text{2R}}{100} + \left(\dfrac{\text{R}}{100}\right)^2 - 1\right] - \text{300R} = 96\\\\ &15000\left[\dfrac{\text{2R}}{100} + \left(\dfrac{\text{R}}{100}\right)^2\right] - \text{300R} = 96\\\\ &300\text{R} + 15000\left(\dfrac{\text{R}}{100}\right)^2 - \text{300R} = 96\\\\ &15000\left(\dfrac{\text{R}}{100}\right)^2= 96\\\\ &15000\left(\dfrac{\text{R}^2}{10000}\right)= 96\\\\ &3\left(\dfrac{\text{R}^2}{2}\right)= 96\\\\ &\text{R}^2 = 64\\\\ &\text{R}= 8\end{align}$MF#%
Rate of interest per annum = 8%
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Solution 2
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The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
$MF#%= \text{P}\left(\dfrac{\text{R}}{100}\right)^2$MF#%