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.
Correct Answer: 8 1/3%
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%