Given banker’s gain, find present worth: The banker’s gain on a sum due 3 years hence at 10% per annum is Rs 36. Find the present worth (PW).

Introduction / Context:
Banker’s gain (BG) equals BD − TD and also equals S * r^2 * t^2 / (1 + r t). From BG we can find the face value S and then the present worth PW = S / (1 + r t).

Given Data / Assumptions:

• BG = Rs 36, r = 10% p.a., t = 3 years.

Concept / Approach:
Use BG = S * r^2 * t^2 / (1 + r t). Compute S, then PW = S / (1 + r t). Here r t = 0.3 and r^2 t^2 = 0.09.

Step-by-Step Solution:

Verification / Alternative check:
BD = S * r * t = 520 * 0.3 = 156; TD = BD / (1 + r t) = 156 / 1.3 = 120; BG = 156 − 120 = 36 ✔️; PW = 520 / 1.3 = 400 ✔️.

Why Other Options Are Wrong:
300, 500, 350 do not make BD − TD equal to 36 at 10% for 3 years.

Common Pitfalls:
Using compound interest; forgetting to divide by (1 + r t) when moving from S to PW.

Final Answer:
Rs 400