Simple Interest – Compare interests to find rate: For the same time period, the simple interest on ₹ 1230 for 2 years is ₹ 10 more than the simple interest on ₹ 1130 for 2 years. What is the annual simple interest rate?

Introduction / Context:
When time is the same, the difference in simple interest is proportional to the difference in principals.

Given Data / Assumptions:

• Difference in principal = 1230 - 1130 = ₹ 100
• Time = 2 years
• Difference in SI = ₹ 10

Concept / Approach:
Let r be annual rate. Then difference in SI = (difference in principal) * r * t.

Step-by-Step Solution:
100 * r * 2 = 10 → 200r = 10 → r = 10/200 = 0.05 = 5%

Verification / Alternative check:
Compute SI for both amounts at 5% for 2 years to confirm a ₹ 10 gap.

Why Other Options Are Wrong:
6%, 8%, 2% do not yield a ₹ 10 difference over 2 years for a ₹ 100 principal gap.

Common Pitfalls:
Using 1 year by mistake or mixing percentage and decimal.

Final Answer:
5%