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The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Options:
A .  Rs. 500
B .  Rs. 400
C .  Rs. 450
D .  Rs. 600
Answer: Option A

Answer : Option A

Explanation :

Let the sum be Rs. P.
Amount after 2 years at 10% per annum when interest is compounded annually
$MF#%= \text{P}\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} = \text{P}\left(1 + \dfrac{10}{100}\right)^2
= \text{P}\left(\dfrac{110}{100}\right)^2 = \text{P}\left(\dfrac{11}{10}\right)^2\\\\ \text{Compound Interest = }\text{P}\left(\dfrac{11}{10}\right)^2 - \text{P} = \text{P}\left[\left(\dfrac{11}{10}\right)^2-1\right]$MF#%
Given that compound interest = 525
$MF#%\begin{align}&\Rightarrow \text{P}\left[\left(\dfrac{11}{10}\right)^2-1\right] = 525\\\\ &\Rightarrow \text{P}\left[\dfrac{121}{100}-1\right] = 525\\\\ &\Rightarrow \text{P}\times \dfrac{21}{100} = 525\\\\ &\Rightarrow \text{P} = 525\times \dfrac{100}{21} = 25 \times 100 = 2500\end{align}$MF#%
Simple interest on the same sum(Rs.2500) for 4 years at 5%
$MF#%= \dfrac{\text{PRT}}{100}=\dfrac{2500 \times 5 \times 4}{100} = 25 \times5 \times 4 = 25 \times 20 =\text{Rs. 500}$MF#%



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