Simple Interest — ₹ 6000 becomes ₹ 8000 in 4 years at simple interest. In how many years at the same rate will ₹ 525 become ₹ 700?

Introduction / Context:
The first pair (₹ 6000 to ₹ 8000 in 4 years) reveals the annual rate under simple interest. That same rate is then applied to a different principal to find the time needed to reach a new amount.

Given Data / Assumptions:

• From ₹ 6000 to ₹ 8000 in 4 years.
• Find t such that ₹ 525 becomes ₹ 700 at the same rate.

Concept / Approach:
From the first pair: SI = 2000 in 4 years ⇒ yearly interest = 500 ⇒ rate r = 500 / 6000 = 1/12 ≈ 8.333% p.a. Then use SI = P * r * t for the second principal.

Step-by-Step Solution:
Needed SI on ₹ 525: 700 − 525 = ₹ 175.P * r * t = 175 ⇒ 525 * (1/12) * t = 175.t = 175 * 12 / 525 = 4 years.

Verification / Alternative check:
At ~8.333% p.a., yearly SI on 525 is 43.75; 4 years produce 175, giving 700.

Why Other Options Are Wrong:
2, 3, 5, 6 years do not generate exactly ₹ 175 interest at this rate.

Common Pitfalls:
Using proportionality with amounts instead of SI; in SI, interest is proportional to time for a fixed rate.

Final Answer:
4 yr