Simple Interest – Rate-gap from interest difference: The difference between the simple interest earned on ₹ 1,000 in 2 years from two banks is ₹ 20. What is the difference between their annual rates of interest?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 1%
Explanation
Introduction / Context:For the same principal and time, the difference in simple interest equals principal * time * difference in rates. This lets us directly compute the rate gap.
Given Data / Assumptions:
- P = ₹ 1000
- t = 2 years
- Difference in SI = ₹ 20
Concept / Approach:Let Δr be the difference in rates (per year as a decimal). Then ΔI = P * t * Δr.
Step-by-Step Solution:20 = 1000 * 2 * ΔrΔr = 20 / 2000 = 0.01 = 1%
Verification / Alternative check:If one bank is 6% and the other 5%, on ₹ 1000 for 2 years the difference is ₹ 20 (matches).
Why Other Options Are Wrong:2%, 1.5%, 2.5% lead to ₹ 40, ₹ 30, and ₹ 50 differences respectively for the same data.
Common Pitfalls:Forgetting that time is 2 years or mixing percent with decimal.
Final Answer:1%