Answer : Option D

Explanation :

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Solution 1
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Let the sum be Rs.x
Amount after 3 years on Rs.x at 20% per annum when interest is compounded annually
$MF#%= \text{P}\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} = \text{x}\left(1 + \dfrac{20}{100}\right)^3 = \text{x}\left(\dfrac{120}{100}\right)^3 = \text{x}\left(\dfrac{6}{5}\right)^3\\\\ \text{Compound Interest = }\text{x}\left(\dfrac{6}{5}\right)^3 - x = x\left[\left(\dfrac{6}{5}\right)^3 - 1\right] = x\left[\dfrac{216}{125} - 1\right] = \dfrac{91x}{125}\\\\ \text{Simple Interest = }\dfrac{\text{PRT}}{100} = \dfrac{x \times 20 \times 3}{100} = \dfrac{3x}{5} $MF#%
Given that difference between compound interest and simple interest is Rs.48
$MF#%\dfrac{91x}{125} - \dfrac{3x}{5} = 48\\\\ \dfrac{91x - 75x}{125} = 48\\\\ \dfrac{16x}{125} = 48\\\\ x = \dfrac{48 \times 125}{16} = 3 \times 125 = \text{Rs. 375}$MF#%
i.e, the sum is Rs.375
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Solution 2
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The difference between compound interest and simple interest on Rs. P for 3 years at R% per annum
$MF#%= \text{P}\left(\dfrac{\text{R}}{100}\right)^2\left(\dfrac{\text{R}}{100}+3\right)$MF#%