A lady borrows a certain principal amount from a bank at 12% simple interest per annum. After 3 years she finds that she has paid Rs 5,400 as interest only. What was the principal amount originally borrowed from the bank?

Introduction / Context:
This question is a direct application of the simple interest formula to find the principal when the interest, rate, and time are known. Such problems are common in banking and loan based aptitude questions because they test whether the candidate can rearrange the simple interest formula correctly and interpret the given data.

Given Data / Assumptions:

• Total simple interest paid, SI = Rs 5,400.
• Rate of interest, R = 12% per annum.
• Time period, T = 3 years.
• Principal, P, is unknown and needs to be calculated.

Concept / Approach:
The basic formula for simple interest is:
SI = (P * R * T) / 100When SI, R, and T are known, we can rearrange the formula to solve for P as:
P = (SI * 100) / (R * T)This is simply algebraic manipulation and is very useful for loan and deposit questions where the original principal must be determined from the interest paid.

Step-by-Step Solution:
Step 1: Write down the formula for principal.P = (SI * 100) / (R * T)Step 2: Substitute SI = 5400, R = 12, and T = 3.P = (5400 * 100) / (12 * 3)Step 3: Simplify the denominator.12 * 3 = 36Step 4: Perform the division.P = (540000) / 36P = 15,000Thus, the principal borrowed was Rs 15,000.

Verification / Alternative check:
We can verify this principal by recomputing the simple interest. With P = Rs 15,000, R = 12% per annum, and T = 3 years:
SI = (15000 * 12 * 3) / 100 = (15000 * 36) / 100 = 540000 / 100 = 5,400The computed interest matches the given interest exactly, confirming that the principal is correct.

Why Other Options Are Wrong:

• Rs 1,50,000 would yield much larger interest than Rs 5,400 at 12% for 3 years.
• Rs 1,500 would give SI = (1500 * 12 * 3) / 100 = 540, which is ten times smaller than required.
• Rs 1,62,000 would again produce an excessively large simple interest, not equal to Rs 5,400.

Common Pitfalls:
Common mistakes include mixing up the roles of principal and interest or forgetting to divide by 100 when applying the percentage formula. Sometimes candidates multiply the interest rate by the time incorrectly or misplace a zero in the calculation. Being systematic, writing each step clearly, and double checking the final multiplication and division help avoid such arithmetic errors.

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