Simple Interest — A sum amounts to ₹ 1012 in 2.5 years and to ₹ 1067.20 in 4 years at simple interest. Find the annual rate.

Introduction / Context:
Two amounts at different times under simple interest allow us to extract the annual interest directly from their difference and then back out the rate.

Given Data / Assumptions:

• A1 = ₹ 1012 at t1 = 2.5 years.
• A2 = ₹ 1067.20 at t2 = 4 years.
• Simple interest applies.

Concept / Approach:
The increase in amount from t1 to t2 equals the extra interest accrued in (t2 − t1) years. That extra interest per year equals P * r.

Step-by-Step Solution:
A2 − A1 = 1067.20 − 1012 = ₹ 55.20 over 1.5 years.Hence annual interest = 55.20 / 1.5 = ₹ 36.80 = P * r.At t1 = 2.5 years, interest = 36.80 * 2.5 = ₹ 92.00, so P = 1012 − 92 = ₹ 920.Therefore r = 36.80 / 920 = 0.04 = 4% per annum.

Verification / Alternative check:
Check A2: Interest in 4 years = 920 * 0.04 * 4 = 147.20; Amount = 920 + 147.20 = 1067.20 (matches).

Why Other Options Are Wrong:
2.5%, 3%, 5%, 6% do not satisfy both amounts simultaneously.

Common Pitfalls:
Assuming the difference depends on changing principal; under SI, principal remains the same.

Final Answer:
4%