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?

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:

Verification / Alternative check:

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.