Simple Interest — Time proportionality: At the same rate, what is the ratio of simple interest earned on the same amount for 12 years and for 18 years?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 2 : 3
Explanation
Introduction / Context:Under simple interest, interest is directly proportional to time when principal and rate are fixed. Ratios of interests for different durations equal the ratios of those durations.
Given Data / Assumptions:
- Same principal and same annual rate
- Two time periods: 12 years and 18 years
Concept / Approach:Let SI1 = P * r * 12 and SI2 = P * r * 18. Then SI1 : SI2 = 12 : 18, which simplifies by dividing both terms by 6.
Step-by-Step Solution:
SI1 : SI2 = (P * r * 12) : (P * r * 18) = 12 : 18.Reduce 12 : 18 by 6 → 2 : 3.Verification / Alternative check:
Pick a trial P and r to confirm numerically (e.g., P = 100, r = 10%): SI1 = 120; SI2 = 180 → 2 : 3.Why Other Options Are Wrong:
- 1 : 3, 2 : 5, 3 : 1, 5 : 2 do not match the proportionality of 12 and 18.
Common Pitfalls:
- Applying compound interest thinking; in SI, proportionality with time is exact.
Final Answer:2 : 3.