A man takes a loan from a bank at 12% per annum simple interest. After 3 years he has to pay Rs. 5,400 as interest only for this period. What was the principal amount borrowed?

Introduction / Context:
This is a straightforward simple interest question where we are given the interest paid over a certain time at a known rate and must find the principal. It is a direct application of the simple interest formula and is very common in banking and finance based aptitude questions.

Given Data / Assumptions:

Rate of simple interest r = 12% per annum.
Time t = 3 years.
Interest paid I = Rs. 5,400 (interest only, not including principal).
We need to find the principal P that was originally borrowed.

Concept / Approach:
The simple interest formula is I = (P * r * t) / 100, where I is interest, P is principal, r is rate percent per annum and t is time in years. When I, r and t are known, we can rearrange to P = (I * 100) / (r * t). This calculation is direct and does not require intermediate steps if we substitute the values correctly.

Step-by-Step Solution:
Given I = 5,400 rupees, r = 12% per annum, t = 3 years. Formula: I = (P * r * t) / 100. So 5,400 = (P * 12 * 3) / 100. Multiply r and t: 12 * 3 = 36. Therefore 5,400 = (36P) / 100. Rearrange for P: P = (5,400 * 100) / 36. Compute numerator: 5,400 * 100 = 540,000. So P = 540,000 / 36 = 15,000.

Verification / Alternative check:
Check using the original formula. With P = 15,000, r = 12% and t = 3, simple interest I = (15,000 * 12 * 3) / 100. Multiply: 15,000 * 36 = 540,000. Then divide by 100 to get 5,400. This matches the interest stated in the question, confirming that the principal is correctly computed.

Why Other Options Are Wrong:
Option Rs.2,000 would produce interest of only (2,000 * 12 * 3) / 100 = 720, which is far below 5,400.
Option Rs.10,000 would yield interest (10,000 * 12 * 3) / 100 = 3,600, again not equal to 5,400.
Option Rs.20,000 gives interest (20,000 * 12 * 3) / 100 = 7,200, which is greater than the stated interest.

Common Pitfalls:
Some learners mistakenly divide by 12 * 3 without multiplying by 100, forgetting that the rate was given as a percentage.
Others treat 12% as 0.12 and substitute directly into a decimal form of the formula but then forget to handle the 100 factor correctly, leading to miscalculation.
Another common error is to confuse simple interest with compound interest and attempt unnecessary repeated percentage calculations over each year.

Final Answer:
The principal amount borrowed from the bank was Rs. 15,000.