Question

A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched ₹5,100 more. The sum is _______.

• A. ₹1,50,000
• B. ₹1,70,000
• C. ₹1,25,000
• D. ₹1,20,000

Hint:

When solving simple interest problems, focus on the difference in interest caused by a change in the rate. This can help directly calculate the principal.

Answer 1

The Correct Option is B

Let the principal amount be \( P \) and the rate of interest be \( r \) percent per annum. The formula for simple interest is: \[ \text{SI} = \frac{P \times r \times t}{100} \] where: - \( P \) is the principal, - \( r \) is the rate of interest, - \( t \) is the time in years. We are told that if the rate of interest had been increased by 1%, the interest would have been ₹5,100 more. This means that the difference in interest due to the 1% increase in rate over 3 years is ₹5,100. Thus, the difference in interest is: \[ \frac{P \times (r + 1) \times 3}{100} - \frac{P \times r \times 3}{100} = 5100 \] Simplifying the above equation: \[ \frac{P \times 3}{100} \times (r + 1 - r) = 5100 \] \[ \frac{3P}{100} = 5100 \] \[ 3P = 5100 \times 100 \] \[ 3P = 510000 \] \[ P = \frac{510000}{3} = 170000 \] Thus, the sum is ₹1,70,000. The correct answer is (2) ₹1,70,000.