A sum of ₹3,000 yields a simple interest of ₹1,080 at 12% per annum. For how many years was the money invested to earn this interest under simple interest?

Introduction:
This question tests solving for time in a simple interest situation. When principal, rate, and interest are known, time can be found by rearranging the standard formula SI = (P * r * t) / 100. Because it is a direct substitution with one rearrangement and no tricky unit conversion (rate is annual and time is asked in years), it is an easy problem.

Given Data / Assumptions:

• Principal P = ₹3,000
• Simple interest SI = ₹1,080
• Rate r = 12% per annum
• Time = t years (unknown)
• 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 carefully. Since r is already a percentage, keep it as 12 (not 0.12) because the formula includes division by 100.

Step-by-Step Solution:
SI = (P * r * t) / 100 t = (SI * 100) / (P * r) t = (1080 * 100) / (3000 * 12) t = 108000 / 36000 t = 3

Verification / Alternative check:
At 12% per year on ₹3000, yearly interest is (3000*12)/100 = 360. Over 3 years, total interest is 360*3 = 1080, matching the given interest exactly.

Why Other Options Are Wrong:
2.5 years would give 360*2.5 = 900. 4 years would give 1440. 5 years would give 1800. Only 3 years produces exactly ₹1080 at 12% on ₹3000.

Common Pitfalls:
Forgetting to multiply SI by 100, using 0.12 and also dividing by 100 again, or confusing amount with interest.

Final Answer:
The money was invested for 3 years.