A sum of Rs. 3000 yields a simple interest of Rs. 1080 at 12% per annum. For how many years is the money invested to earn this interest?

Introduction / Context:
This is a straightforward simple interest question where you are given the principal, the rate of interest per annum, and the total simple interest earned. The objective is to find the time period in years. Such problems reinforce your comfort with rearranging the simple interest formula to solve for time and also give good practice in basic arithmetic manipulation under exam conditions.

Given Data / Assumptions:

• Principal P = Rs. 3000.
• Total simple interest SI = Rs. 1080.
• Rate of interest R = 12% per annum.
• Interest is calculated as simple interest with a constant rate.

Concept / Approach:
The simple interest formula is SI = P * R * T / 100, where T is the time in years. We are asked to find T, and we know SI, P, and R. Rearranging the formula gives T = SI * 100 / (P * R). Substituting the numerical values into this expression will give the time period directly. Finally, we verify that the computed time leads back to the correct interest of Rs. 1080 to ensure that no arithmetic mistakes were made.

Step-by-Step Solution:
Step 1: Write the simple interest formula: SI = P * R * T / 100. Step 2: Substitute SI = 1080, P = 3000, R = 12. Step 3: 1080 = 3000 * 12 * T / 100. Step 4: Simplify 3000 * 12 / 100 = 3000 * 0.12 = 360. Step 5: So 1080 = 360 * T. Step 6: Solve for T by dividing both sides by 360: T = 1080 / 360. Step 7: 1080 / 360 = 3. Step 8: Therefore, the time period is 3 years.

Verification / Alternative check:
To verify, compute the interest using T = 3 years. SI = 3000 * 12 * 3 / 100 = 3000 * 36 / 100 = 3000 * 0.36 = 1080. This exactly matches the given interest in the question. Therefore, T = 3 years is correct. Such reverse checking is quick and very helpful in multiple-choice questions to confirm that the chosen answer is accurate.

Why Other Options Are Wrong:
If T = 4 years, SI would be 3000 * 12 * 4 / 100 = 1440, which is too high. If T = 5 years, SI becomes 1800. If T = 2.5 years, SI is 3000 * 12 * 2.5 / 100 = 900, which is too low. Only when T = 3 years do we get the correct interest of Rs. 1080, so the other options cannot be correct.

Common Pitfalls:
Some students mistakenly plug values into a rearranged formula without checking each step, leading to sign or division errors. Others confuse simple interest with compound interest and try to use powers instead of the linear formula. Another minor error is miscalculating 3000 * 12 / 100. Being systematic and verifying with a quick re-calculation of SI helps avoid such mistakes.

Final Answer:
The money is invested for a period of 3 Years.