Question

Rakesh invests a certain sum at a certain rate with simple interest for 4 years. Had he invested it at 2% higher, he would have earned Rs.240 more. Find the sum he invested

• A. Rs. 1800
• B. Rs. 2400
• C. Rs. 3000
• D. Rs. 3600

Hint:

Principal $P = \frac{\Delta SI \times 100}{\Delta R \times T} = \frac{240 \times 100}{2 \times 4} = \text{Rs. } 3000$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Under simple interest, the additional interest earned is directly generated by the incremental interest rate on the principal.

Step 2: Key Formula or Approach:
Let the principal be $P$.
Additional interest rate $\Delta R = 2\%$, Time $T = 4\,\text{years}$, Additional Interest $\Delta SI = \text{Rs. } 240$.
The formula relating additional interest to principal is:
\[\Delta SI = \frac{P \times \Delta R \times T}{100}\]

Step 3: Detailed Explanation:
Substituting the values:
\[240 = \frac{P \times 2 \times 4}{100} = \frac{8P}{100} \implies P = \frac{240 \times 100}{8} = 3000\]

Step 4: Final Answer:
Therefore, the sum invested was Rs. 3000.