The present worth (PW) of a certain sum due sometime hence is ₹3400 and the true discount (TD) is ₹340. Find the banker’s gain (BG).

Introduction / Context:
Given PW and TD, we can compute x = TD / PW because TD = x * PW. Banker’s gain then equals BG = x * TD = x^2 * PW. This provides BG directly without full details of rate and time.

Given Data / Assumptions:

• PW = ₹3400.
• TD = ₹340.

Concept / Approach:
Compute x = TD / PW. Then BG = x * TD. Alternatively, BG = TD^2 / PW, which is the same identity rearranged.

Step-by-Step Solution:

Verification / Alternative check:
Using BG = TD^2 / PW = 340^2 / 3400 = 115600 / 3400 = ₹34; consistent.

Why Other Options Are Wrong:
₹17, ₹18, and ₹21 are not equal to TD^2 / PW.

Common Pitfalls:
Confusing BG with BD − TD when BD is not given; here the formula avoids BD entirely.

Final Answer:
Rs. 34