The simple interest accrued on an amount of Rs 28,500 over a period of 7 years is Rs 23,940; what is the annual rate of simple interest in percent per annum for this investment?

Introduction / Context:
This problem provides the principal, the time period, and the total simple interest earned, and asks for the annual simple interest rate. It tests direct use of the simple interest formula rearranged to solve for the rate. Such questions are typical when analysing bank deposits, loans, or fixed deposits in aptitude and competitive exams.

Given Data / Assumptions:
- Principal P = Rs 28,500. - Simple interest earned SI = Rs 23,940. - Time period T = 7 years. - Annual rate of simple interest R in percent per annum is unknown. - Interest is calculated using simple interest, no compounding is involved.

Concept / Approach:
The simple interest formula SI = (P * R * T) / 100 can be rearranged to find the rate as R = (SI * 100) / (P * T). By plugging in the known values for SI, P, and T, we directly compute the percentage rate. Because all values are whole numbers, the calculation is straightforward and the result is a clean percentage.

Step-by-Step Solution:
Step 1: Start with SI = (P * R * T) / 100. Step 2: Rearrange for R: R = (SI * 100) / (P * T). Step 3: Substitute SI = 23,940, P = 28,500, T = 7. Step 4: Compute denominator P * T = 28,500 * 7 = 1,99,500. Step 5: Compute numerator SI * 100 = 23,940 * 100 = 23,94,000. Step 6: Divide numerator by denominator: R = 23,94,000 / 1,99,500. Step 7: Perform the division: 23,94,000 / 1,99,500 = 12. Step 8: Therefore, R = 12 percent per annum.

Verification / Alternative check:
Verify by recomputing the simple interest using R = 12 percent. SI = (28,500 * 12 * 7) / 100. First 28,500 * 12 = 3,42,000. Then 3,42,000 * 7 = 23,94,000. Dividing by 100 gives SI = Rs 23,940, which exactly matches the given interest. Hence, the rate of 12 percent per annum is confirmed as correct.

Why Other Options Are Wrong:
At 10.5 percent, SI would be (28,500 * 10.5 * 7) / 100, which is significantly less than Rs 23,940. At 12.5 percent, the interest would be slightly larger than 23,940. At 11 percent, interest is again lower than needed. Only 12 percent produces exactly Rs 23,940 over 7 years on Rs 28,500.

Common Pitfalls:
Candidates sometimes forget to multiply by 100 in the numerator when solving for R, which gives a rate that is too small. Another mistake is to divide the simple interest by time alone instead of by principal times time. Writing the formula explicitly and substituting step by step helps prevent these errors.

Final Answer:
The annual rate of simple interest is 12% per annum.