For what time t (in years) will the simple interest on Rs 400 at 10% per annum equal the simple interest on Rs 1000 for 4 years at 4% per annum?

Introduction / Context:
Equate two simple-interest amounts. For SI, I = P * R * T (with R in per-year fraction). Solve for the unknown time t.

Given Data / Assumptions:

• I1 (on Rs 400 at 10% for t years) = 400 * 0.10 * t.
• I2 (on Rs 1000 at 4% for 4 years) = 1000 * 0.04 * 4.

Concept / Approach:
Set I1 = I2 and solve for t.

Step-by-Step Solution:
400 * 0.10 * t = 1000 * 0.04 * 4 → 40 t = 160 → t = 4 years.

Verification / Alternative check:
I1 = 40*4 = 160; I2 = 1000*0.16 = 160; equal.

Why Other Options Are Wrong:
2, 3, 6 years give mismatched interest amounts.

Common Pitfalls:
Mixing percentage and decimal forms; forgetting to multiply 4% by 4 years.

Final Answer:
4 yrs