Simple Interest – Rate from interest difference on ₹ 1,200 vs ₹ 1,000 over 3 years: The interest on ₹ 1,200 exceeds the interest on ₹ 1,000 by ₹ 50 in 3 years at the same rate. Find the annual rate percent.

Introduction / Context:
With simple interest at the same rate, the extra interest earned by a higher principal over a fixed time equals the interest on the principal difference. This allows direct computation of the rate from the stated rupee difference.

Given Data / Assumptions:

• P1 = ₹ 1,200, P2 = ₹ 1,000
• Time t = 3 years
• Interest difference ΔI = ₹ 50
• Common rate r% per annum

Concept / Approach:
The difference in interest equals (P1 − P2) * r * t / 100. Solve r from ΔI and the known difference in principal and time.

Step-by-Step Solution:
ΔP = 1,200 − 1,000 = 200ΔI = 200 * r * 3 / 100 = 6rSet 6r = 50 ⇒ r = 50 / 6 = 8 1/3%

Verification / Alternative check:
Compute interests at r = 8 1/3%: I1 − I2 = (200 * 8 1/3 * 3) / 100 = 50, validating the result.

Why Other Options Are Wrong:
10 1/3%, 6 2/3%, and 9 2/3% produce differences not equal to ₹ 50 over 3 years for a ₹ 200 principal gap; 7 1/2% also does not match.

Common Pitfalls:
Ignoring that both loans share the same rate leads to unnecessary system solving. Use the principal difference directly.

Final Answer:
8 1/3%