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
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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