A lady borrows a certain principal amount from a bank at 12% simple interest per annum and after 3 years finds that she has paid Rs 5,400 as interest only; what was the original principal amount borrowed from the bank under this simple interest agreement?

Introduction / Context:
This is a straightforward simple interest problem where the total interest paid over a fixed time and rate is known and the task is to find the original principal borrowed. Such questions are common in aptitude tests to check whether candidates can rearrange the simple interest formula to solve for the principal. The context of a bank loan makes the scenario realistic and relatable.

Given Data / Assumptions:
- Total simple interest paid SI = Rs 5,400. - Annual simple interest rate R = 12 percent per annum. - Time period T = 3 years. - Principal P (the amount borrowed) is unknown. - Interest is calculated strictly using the simple interest formula.

Concept / Approach:
The basic formula for simple interest is SI = (P * R * T) / 100. Here we need to find P, so we rearrange the formula to P = (SI * 100) / (R * T). By substituting the given values of SI, R, and T into this rearranged formula, we can compute the original loan amount. No compounding or additional charges are involved in this idealised calculation.

Step-by-Step Solution:
Step 1: Start from SI = (P * R * T) / 100. Step 2: Rearrange to find principal: P = (SI * 100) / (R * T). Step 3: Substitute SI = 5,400, R = 12, and T = 3. Step 4: Compute denominator R * T = 12 * 3 = 36. Step 5: Compute numerator SI * 100 = 5,400 * 100 = 5,40,000. Step 6: Divide: P = 5,40,000 / 36. Step 7: Perform the division: 5,40,000 / 36 = 15,000. Step 8: Therefore, the principal amount borrowed from the bank is Rs 15,000.

Verification / Alternative check:
Verify by computing the simple interest on P = Rs 15,000 for 3 years at 12 percent per annum. SI = (15,000 * 12 * 3) / 100. First 15,000 * 12 = 1,80,000. Then 1,80,000 * 3 = 5,40,000. Dividing by 100 gives SI = Rs 5,400, which matches the interest given in the question. This confirms that the calculated principal is correct.

Why Other Options Are Wrong:
If P were Rs 1,50,000, the interest would be ten times larger, that is Rs 54,000, not Rs 5,400. A principal of Rs 1,500 would give SI = (1,500 * 12 * 3) / 100 = Rs 540, which is too small. A principal of Rs 1,62,000 would produce an interest far greater than Rs 5,400. Only Rs 15,000 leads to the correct interest amount.

Common Pitfalls:
Some learners mistakenly divide by 100 twice or forget to multiply the interest by 100 while isolating the principal. Others may mix up the roles of SI and P in the formula. Writing the rearranged expression P = SI * 100 / (R * T) clearly before substituting values helps avoid such algebraic errors.

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