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?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 4 yrs
Explanation
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