Simple Interest – Find rate percent from two amounts: A sum amounts to Rs 1,260 in 2 years and to Rs 1,350 in 5 years at simple interest. Find the annual rate of interest (percent per annum).
Aptitude
Simple Interest
Difficulty: Medium
Choose an option
Answer
Correct Answer: 2.5%
Explanation
Introduction / Context:Two amounts at two times under SI directly reveal the uniform annual interest, enabling calculation of both principal and rate. Here, only the rate is asked.
Given Data / Assumptions:
- A2 = Rs 1260 (t = 2 years)
- A5 = Rs 1350 (t = 5 years)
Concept / Approach:Annual SI = (A5 - A2) / (5 - 2). Principal P = A2 - 2 * (annual SI). Rate r% = (annual SI / P) * 100.
Step-by-Step Solution:
Annual SI = (1350 - 1260) / 3 = 90 / 3 = Rs 30Principal P = 1260 - 2 * 30 = Rs 1200Rate r% = (30 / 1200) * 100 = 2.5%Verification / Alternative check:
Check A5 = 1200 * (1 + 0.025 * 5) = 1200 * 1.125 = 1350 (matches)Why Other Options Are Wrong:
- 30% / 10% / 5% / 7.5%: do not fit the computed annual increase and principal.
Common Pitfalls:
- Dividing by total time instead of the time gap between the two amounts.
- Using compound interest logic.
Final Answer:2.5% per annum.