A certain sum of money fetches a total simple interest of ₹5,400 at the rate of 12.5% per annum in 4 years. What is the principal sum (in rupees)?

Introduction:
This is a direct simple interest calculation where interest, rate, and time are given and you must find the principal. The simple interest formula can be rearranged to compute principal as P = (SI * 100) / (r * t). Because it is straightforward substitution with one rearrangement, it is an easy problem.

Given Data / Assumptions:

• Simple interest SI = ₹5,400
• Rate r = 12.5% per annum
• Time t = 4 years
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Rearrange the simple interest formula to isolate P: P = (SI * 100) / (r * t). Substitute the values and compute carefully. Since the rate is given in percent, the factor 100 in the formula is already accounted for by dividing by 100 (or multiplying SI by 100 when solving for P).

Step-by-Step Solution:
SI = (P * r * t) / 100 P = (SI * 100) / (r * t) P = (5400 * 100) / (12.5 * 4) Denominator: 12.5 * 4 = 50 P = 540000 / 50 = 10800

Verification / Alternative check:
If P = 10800, then SI = (10800 * 12.5 * 4)/100. Since 12.5*4 = 50, SI = (10800 * 50)/100 = 5400, matching the given interest exactly.

Why Other Options Are Wrong:
Any other principal value would produce an SI different from ₹5,400 because SI is directly proportional to P for fixed r and t.

Common Pitfalls:
Using 0.125 in place of 12.5 while still dividing by 100 again, or forgetting to multiply SI by 100 when rearranging for P.

Final Answer:
The principal sum is ₹10,800.