The banker’s gain (BG) on a certain sum due 2 years hence at 10% p.a. is ₹24. What is the present worth (PW)?

Introduction / Context:
With BG and x known, PW follows from BG = x^2 * PW. This method is efficient because it does not require determining face value first or computing TD separately unless desired for checking.

Given Data / Assumptions:

• r = 10% p.a., t = 2 years ⇒ x = 0.20.
• BG = ₹24.

Concept / Approach:
Use BG = x^2 * PW. Thus PW = BG / x^2. Straight substitution yields the answer immediately.

Step-by-Step Solution:

Verification / Alternative check:
TD = x * PW = 0.2 * 600 = ₹120; BG = x * TD = 0.2 * 120 = ₹24, correct.

Why Other Options Are Wrong:
₹300, ₹400, ₹500 produce BG values different from ₹24 when multiplied by x^2 = 0.04.

Common Pitfalls:
Using BD or other intermediate steps unnecessarily; the direct identity suffices.

Final Answer:
Rs. 600