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 Rs.5,100 more. The sum is ........

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

Hint:

When solving simple interest problems involving percentage changes, focus on the difference in interest due to the change in rate, and use that to form an equation for the principal amount.

Answer 1

The Correct Option is B

Let the sum be \( P \) and the rate of interest be \( R \) % per annum. The simple interest for 3 years is given by the formula: \[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \] Where: - \( P \) is the principal amount, - \( R \) is the rate of interest, - \( T \) is the time in years. Given: - \( T = 3 \) years, - The increase in interest is Rs.5,100 when the rate is increased by 1% (from \( R \) to \( R+1 \)). So, the difference in interest is: \[ \text{Difference in interest} = \frac{P \times (R + 1) \times 3}{100} - \frac{P \times R \times 3}{100} = 5100 \] \[ \frac{P \times 3}{100} = 5100 \] \[ P = \frac{5100 \times 100}{3} = 1,70,000 \]

Step 2: Final Answer The correct answer is (b) Rs.1,70,000. Final Answer: The correct answer is (b) Rs.1,70,000.