Simple Interest – Combine two loans at one rate: Raju lends ₹ 400 to Ajay for 2 years and ₹ 100 to Manoj for 4 years. He receives a total of ₹ 60 as simple interest from both. What is the annual simple interest rate?

Introduction / Context:
When multiple loans share the same rate but differ in principal and time, the total simple interest is the sum of P * r * t for each component.

Given Data / Assumptions:

• Loan 1: ₹ 400 for 2 years
• Loan 2: ₹ 100 for 4 years
• Total SI = ₹ 60; rate r is the same for both

Concept / Approach:
Total SI = r * (400 * 2 + 100 * 4) = r * (800 + 400) = 1200r.

Step-by-Step Solution:
1200 r = 60 → r = 60 / 1200 = 0.05 = 5%

Verification / Alternative check:
At 5%: SI1 = 400 * 0.05 * 2 = 40; SI2 = 100 * 0.05 * 4 = 20; total = 60.

Why Other Options Are Wrong:
6%, 8%, 9% lead to totals 72, 96, and 108 respectively, not ₹ 60.

Common Pitfalls:
Not summing the time-weighted principals or using compound interest erroneously.

Final Answer:
5%