Question : A man borrowed some money from a private organisation at 5% simple interest per annum. He lent this money to another person at 10% compound interest per annum and made a profit of Rs. 26,410 in 4 years, the man borrowed:
Option 1: Rs. 2,00,000
Option 2: Rs. 1,50,000
Option 3: Rs. 1,32,050
Option 4: Rs. 1,00,000
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Correct Answer: Rs. 1,00,000
Solution : Simple interest for Rs. 100 for 4 years at 5% interest rate (SI) = $\frac{100\times5\times 4}{100}$ = Rs. 20 The amount accrued for Rs. 100 for 4 years at 10% compound interest = $100(1+\frac{10}{100})^4$ = Rs. 146. 41 So, the compound interest (CI) = Rs. (146.41 – 100) = Rs. 46.41 ⇒ Difference between CI and SI = Rs. 26.41 If the difference is Rs. 26,410, then the principal = $\frac{100 }{26.41} \times 26410$ = Rs. 1,00,000 Hence, the correct answer is Rs. 1,00,000.
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