How much time (in years) will it take for a principal of ₹450 to earn ₹81 as simple interest at an annual rate of 4.5% per annum?

Introduction:
This question tests direct use of the simple interest formula to find time. When principal, interest, and rate are known, time can be computed by rearranging SI = (P * r * t) / 100. Because it is a single formula substitution with no tricky conversions (rate is annual and time is requested in years), this is an easy-level problem.

Given Data / Assumptions:

• Principal P = ₹450
• Simple interest SI = ₹81
• Rate r = 4.5% per annum
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Rearrange the formula to isolate t: t = (SI * 100) / (P * r). Substitute the given values and compute. Ensure that the rate is used as a percentage (not decimal) because the formula already divides by 100.

Step-by-Step Solution:
SI = (P * r * t) / 100 t = (SI * 100) / (P * r) t = (81 * 100) / (450 * 4.5) t = 8100 / 2025 t = 4

Verification / Alternative check:
Check by forward calculation: SI = (450 * 4.5 * 4) / 100 = (450 * 18) / 100 = 8100 / 100 = ₹81, which matches exactly.

Why Other Options Are Wrong:
3 years and 3.5 years give less than ₹81. 4.5 and 5 years give more than ₹81 because interest increases linearly with time at simple interest.

Common Pitfalls:
Using 0.045 instead of 4.5 while still dividing by 100 (double division), or mixing months and years without converting (not needed here).

Final Answer:
It will take 4 years.