Question : If the difference between the simple interest and the compound interest for 3 years at the rate of 10% per annum on a certain sum is equal to Rs. 310, then that sum of money is:
Option 1: Rs. 8,000
Option 2: Rs. 9,500
Option 3: Rs. 12,000
Option 4: Rs. 10,000
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Correct Answer: Rs. 10,000
Solution :
Given: The difference between the simple interest and the compound interest = Rs. 310
R = 10 %
Time = 3 years
Let the sum be $P$.
$P(1+\frac{10}{100})^{3}–P–(\frac{P×10×3}{100})=310$
⇒ $P[(\frac{11}{10})^{3}–1–\frac{3}{10}]=310$
⇒ $P[(\frac{1331–1000-300}{1000})]=310$
⇒ $P[(\frac{31}{1000})]=310$
⇒ $P=\frac{310×1000}{31}$
⇒ $P=10000$
Hence, the correct answer is Rs. 10,000.
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