Difference between SI and TD over 6 months at 12.5% is Rs 25: find face value: For a certain sum, the difference between Simple Interest (on the face value) and True Discount for 6 months at 12.5% p.a. equals Rs 25. Find the face value (sum due).

Introduction / Context:
A useful identity is that SI − TD for the same sum, time, and rate equals the banker’s gain (BG) = S * r^2 * t^2 / (1 + r t). Using the given difference, we can solve for S directly.

Given Data / Assumptions:
r = 12.5% = 0.125; t = 6 months = 0.5 year; SI − TD = Rs 25.

Concept / Approach:
BG = S * r^2 * t^2 / (1 + r t) = 25. Compute r t and r^2 t^2, then solve for S.

Step-by-Step Solution:

Verification / Alternative check:
SI = S r t = 6800 * 0.0625 = 425. TD = SI / (1 + r t) = 425 / 1.0625 = 400. Difference = 25 ✔️.

Why Other Options Are Wrong:
6500, 6000, 6200 do not yield a difference of 25 between SI and TD at given r and t.

Common Pitfalls:
Confusing TD with BD; forgetting the 1 + r t denominator in BG.

Final Answer:
Rs 6,800