Simple Interest – Find principal from change in rate: A sum was invested for 4 years. If the annual simple interest rate had been 2% higher, the total interest would have been ₹ 56 more. What is the principal?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: ₹ 700
Explanation
Introduction / Context:In simple interest, increasing the rate by a fixed percentage changes the total interest linearly with principal and time.
Given Data / Assumptions:
- Time t = 4 years
- Rate increase Δr = 2% = 0.02
- Extra interest ΔI = ₹ 56
Concept / Approach:ΔI = P * Δr * t. Solve for P.
Step-by-Step Solution:56 = P * 0.02 * 4 = 0.08 PP = 56 / 0.08 = 700
Verification / Alternative check:At principal ₹ 700, extra per year = 2% of 700 = 14; over 4 years → ₹ 56 (matches).
Why Other Options Are Wrong:₹ 680, ₹ 720, ₹ 820 give extra interest not equal to ₹ 56.
Common Pitfalls:Using compound interest thinking or forgetting to convert 2% into decimal.
Final Answer:₹ 700