A sum of money placed at simple interest at a rate of 13.5% per annum amounts to ₹2,502.50 after 4 years. What is the original principal (initial sum) invested?

Introduction:
This problem tests how to find the principal when the final amount is given under simple interest. Under simple interest, the amount A equals principal plus interest, and interest is linear in time. We use A = P * (1 + r*t/100) and solve for P. Because it is one main formula with careful percentage handling, it is medium difficulty.

Given Data / Assumptions:

• Final amount A = ₹2,502.50
• Rate r = 13.5% per annum
• Time t = 4 years
• Simple interest amount formula: A = P * (1 + r*t/100)

Concept / Approach:
Compute the interest factor (1 + r*t/100). Then divide the amount by this factor to get P. Ensure the rate is treated as 13.5 (not 0.135) because the formula already divides by 100.

Step-by-Step Solution:
A = P * (1 + r*t/100) Compute r*t/100 = (13.5 * 4) / 100 = 54 / 100 = 0.54 So A = P * (1 + 0.54) = 1.54P P = A / 1.54 = 2502.50 / 1.54 P = 1625

Verification / Alternative check:
Compute SI = (P * r * t)/100 = (1625 * 13.5 * 4)/100 = 1625 * 0.54 = 877.50. Amount = 1625 + 877.50 = 2502.50, matching perfectly.

Why Other Options Are Wrong:
₹1,525 and ₹1,425 would produce a smaller amount than ₹2,502.50 at the same rate and time. ₹1,700 would produce a larger amount. ₹1,325 is too low by a large margin.

Common Pitfalls:
Using 0.135 in place of 13.5 while still dividing by 100, or mistakenly compounding interest rather than using the linear simple interest amount formula.

Final Answer:
The original principal is ₹1,625.