Simple Interest – Determine rate from two amounts at 2 and 5 years: A sum amounts to ₹ 1,260 in 2 years and ₹ 1,350 in 5 years under simple interest. Find the rate per cent per annum.

Introduction / Context:
The difference between amounts under simple interest over different times reveals the constant annual interest. From that, we can deduce both principal and rate. Here we only need the rate per annum.

Given Data / Assumptions:

• A(2 yr) = ₹ 1,260
• A(5 yr) = ₹ 1,350
• Simple interest: linear increase per year

Concept / Approach:
Difference over 3 years is 1,350 − 1,260 = 90, so annual interest is 90 / 3 = 30. Then deduce principal from A(2 yr) and compute r = (annual interest / principal) * 100.

Step-by-Step Solution:
Annual interest = (1,350 − 1,260) / 3 = 30Let P be principal; A(2 yr) = P + 2*30 = 1,260 ⇒ P = 1,200Rate r = (30 / 1,200) * 100 = 2.5%

Verification / Alternative check:
Check A(5 yr) = 1,200 + 5*30 = 1,350, consistent with the given values. Therefore r = 2.5% is correct.

Why Other Options Are Wrong:
3.75%, 5%, and 7.5% imply annual interest values inconsistent with the observed differences between 2 and 5 years.

Common Pitfalls:
Using compound growth or mixing up the units (months vs years) will produce incorrect rates in simple-interest settings.

Final Answer:
2.5%