Question

A certain amount earns simple interest of Rs. 2,550 after 8 years. Had the rate of interest been 3% more, how much interest would it have earned?

• A. Rs. 360
• B. Rs. 435
• C. Rs. 285
• D. Can`t be determined

Hint:

In simple interest problems, make sure to gather all necessary information, such as the principal amount and the rate of interest. If any key details are missing, the answer cannot be determined.

Answer 1

The Correct Option is D

Let the principal amount be \( P \) and the rate of interest be \( R % \). Step 1: Use the simple interest formula to find the principal.
The simple interest formula is: \[ SI = \frac{P \times R \times T}{100} \] Given that \( SI = 2,550 \) and \( T = 8 \) years, we can substitute these values into the formula: \[ 2,550 = \frac{P \times R \times 8}{100} \] Simplifying: \[ 2,550 = \frac{8P \times R}{100} \quad \Rightarrow \quad 2,550 \times 100 = 8P \times R \quad \Rightarrow \quad 255,000 = 8P \times R \] \[ P \times R = \frac{255,000}{8} = 31,875 \]

Step 2: Increase the rate by 3%.
The new rate of interest becomes \( R + 3 \). The interest with this increased rate can be calculated as: \[ SI_{\text{new}} = \frac{P \times (R + 3) \times 8}{100} \] Substitute \( P \times R = 31,875 \) into the formula: \[ SI_{\text{new}} = \frac{31,875 \times 8 + 3 \times P \times 8}{100} \] We can see that to calculate the new simple interest, we need to know the exact value of \( P \). Since we don`t have enough information to determine the principal \( P \), the new interest can`t be determined. Final Answer: The correct answer is (d) Can`t be determined.