On a principal of ₹3,500 invested at a simple interest rate of 7% per annum, ₹500 is earned as interest in a certain number of years. For the same time period, what annual rate of simple interest is required on ₹4,900 so that the interest earned becomes ₹800?

Introduction:
This question tests the core idea of simple interest (SI) and how the same time period can be reused to find a new interest rate. In simple interest, interest grows linearly with principal, rate, and time, so we can first compute the time from the first investment and then reuse that time to find the required rate in the second investment.

Given Data / Assumptions:

• First case: P1 = ₹3,500, r1 = 7% per annum, SI1 = ₹500
• Second case: P2 = ₹4,900, SI2 = ₹800
• Time period is the same in both cases
• Simple interest formula: SI = (P * r * t) / 100

Concept / Approach:
Step 1: Use the first case to compute time t. Step 2: Substitute the same t into the second case and solve for the unknown rate r2. Since SI is directly proportional to r when P and t are fixed, the calculation becomes straightforward after t is known.

Step-by-Step Solution:
From SI = (P * r * t) / 100, we get t = (SI * 100) / (P * r) t = (500 * 100) / (3500 * 7) t = 50000 / 24500 = 100 / 49 years (approximately 2.0408 years) Now use SI2 = (P2 * r2 * t) / 100 800 = (4900 * r2 * (100/49)) / 100 800 = (4900 * r2) / 49 r2 = (800 * 49) / 4900 = 8

Verification / Alternative check:
Using proportionality: with same time, SI is proportional to P*r. Compare the two cases: SI1 corresponds to 3500*7, and SI2 corresponds to 4900*r2. Solving gives the same result r2 = 8%.

Why Other Options Are Wrong:
7.5% and 8.5% are close distractors but do not produce exactly ₹800 for the same time. 9% gives too much interest, and 6.5% gives too little.

Common Pitfalls:
Forgetting that the time period is the same, mixing up simple interest with compound interest, or using years incorrectly without computing t from the first scenario.

Final Answer:
The required simple interest rate is 8% per annum.