A certain sum of money fetches a total simple interest of Rs. 5400 at the rate of 12.5% per year in 4 years. What is the principal sum (in rupees)?

Introduction / Context:
This is a direct application of the simple interest formula where you are given the total interest, the rate of interest per annum, and the time period in years. The goal is to find the original principal sum. Such questions are common in aptitude exams and banking tests because they check whether you can rearrange the simple interest formula correctly to solve for the principal when other quantities are known.

Given Data / Assumptions:

• Total simple interest SI = Rs. 5400.
• Rate of interest R = 12.5% per annum.
• Time period T = 4 years.
• Interest is calculated using simple interest, not compounding.
• The rate remains constant over the entire period.

Concept / Approach:
The standard formula for simple interest is SI = P * R * T / 100, where P is principal, R is rate per annum in percent, and T is time in years. When SI, R, and T are known, we can rearrange the formula to find P: P = SI * 100 / (R * T). The only careful step here is handling the decimal rate 12.5%, which we use numerically as 12.5 without any special tricks. After computing P, we check whether this principal, when used in the formula, reproduces the given interest of Rs. 5400.

Step-by-Step Solution:
Step 1: Write the formula for simple interest: SI = P * R * T / 100. Step 2: Substitute SI = 5400, R = 12.5, and T = 4 years. Step 3: So 5400 = P * 12.5 * 4 / 100. Step 4: Simplify the denominator: 12.5 * 4 = 50. Step 5: Therefore 5400 = P * 50 / 100. Step 6: P * 50 / 100 = P * 0.5. Step 7: So 5400 = 0.5 * P. Step 8: Rearranging, P = 5400 / 0.5 = 10800. Step 9: Hence, the principal sum is Rs. 10800.

Verification / Alternative check:
We verify by computing the interest on P = 10800. Using SI = P * R * T / 100, we get SI = 10800 * 12.5 * 4 / 100. First compute 12.5 * 4 = 50. Then SI = 10800 * 50 / 100 = 10800 * 0.5 = 5400. This matches the given total interest, confirming that the principal is correct. This quick verification ensures we did not make any arithmetic mistakes while manipulating the formula.

Why Other Options Are Wrong:
For P = 11800, SI would be 11800 * 12.5 * 4 / 100 = 5900, which is too high. For P = 12800, SI becomes 6400, also incorrect. For P = 9800, SI would be 9800 * 12.5 * 4 / 100 = 4900, which is less than the required 5400. Only P = 10800 produces exactly Rs. 5400 as simple interest for the given rate and time.

Common Pitfalls:
A common mistake is mishandling the rate 12.5%, such as converting it incorrectly or forgetting that it is already a percentage. Another frequent error is misplacing the factors in the formula when solving for P, for example, dividing by 100 incorrectly or not multiplying all parts. Careful algebraic rearrangement and step-by-step substitution help avoid these mistakes, especially under time pressure in exams.

Final Answer:
The principal sum that yields Rs. 5400 as simple interest is Rs. 10800.