Simple Interest – Find rate from two amounts at different times: A certain sum amounts to ₹ 575 in 3 years and ₹ 625 in 5 years under simple interest. Determine the annual rate of interest.

Introduction / Context:
When amounts at two different times are known under simple interest, the yearly interest can be deduced from their difference because simple interest adds a fixed amount each year. This yields both the annual interest and then the rate relative to principal.

Given Data / Assumptions:

• A(3 yr) = ₹ 575
• A(5 yr) = ₹ 625
• Simple interest adds a constant amount per year

Concept / Approach:
The difference in amounts over 2 years equals 2 times the annual interest. Use that to get the yearly interest, back-find principal from one amount, and compute the rate r = (annual interest / principal) * 100.

Step-by-Step Solution:
Difference over 2 years = 625 − 575 = 50Annual interest = 50 / 2 = 25Let P be principal; A(3 yr) = P + 3 * 25 = 575 ⇒ P = 575 − 75 = 500Rate r = (25 / 500) * 100 = 5%

Verification / Alternative check:
Check A(5 yr) = 500 + 5 * 25 = 625, consistent with data. Hence r = 5% is confirmed.

Why Other Options Are Wrong:
3% and 4% yield too small an annual interest; 7% is too large relative to the observed differences.

Common Pitfalls:
Confusing amount differences with principal differences or assuming compound growth leads to incorrect inferences. Remember SI adds linearly per year.

Final Answer:
5%