Question : If the difference between the compound interest and simple interest on a sum of money for 3 years is Rs. 186, find the sum of money, if the interest rate in both cases is 10%.
Option 1: Rs. 5,500
Option 2: Rs. 7,200
Option 3: Rs. 6,500
Option 4: Rs. 6,000
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Correct Answer: Rs. 6,000
Solution :
Given: Difference = Rs. 186
Rate = 10%
Time = 3 years
By applying the formula for finding the difference between CI and SI:
Difference = Principal$(\frac{R}{100})^2(\frac{R}{100}+3)$
⇒ 186 = Principal$(\frac{10}{100})^2(\frac{10}{100}+3)$
⇒ 186 = Principal$(\frac{1}{10})^2(\frac{1}{10}+3)$
⇒ 186 = Principal$(\frac{1}{100})(\frac{31}{10})$
Principal = $(\frac{186×10×100}{31})$ = 6000
Hence, the correct answer is Rs. 6,000.
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