Question : In how many years will the simple interest on a sum of Rs. 6000 lent at 5% per annum be equal to the simple interest on a sum of Rs. 2000 lent for 30 years at 4% per annum?
Option 1: 6 years
Option 2: 12 years
Option 3: 20 years
Option 4: 8 years
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Correct Answer: 8 years
Solution : Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ We are given that the simple interest on Rs. 6000 at 5% per annum is equal to the simple interest on Rs. 2000 at 4% per annum for 30 years. So, we can set up the equation, $⇒6000 \times \frac{5}{100} \times T = 2000 \times \frac{4}{100} \times 30$ $⇒60 \times5T = 20 \times 4 \times 30$ $⇒T = 8 \, \text{years}$ Hence, the correct answer is 8 years.
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