Present Worth and Banker’s Gain known → True Discount: The present worth of a sum due some time hence is Rs. 576 and the banker's gain is Re. 1. What is the true discount?

Introduction / Context:
With simple interest, BG = F * x^2 / (1 + x) and P = F / (1 + x), where x = r * t. If P and BG are known, x can be determined first, then TD = F * x / (1 + x) or simply TD = F − P.

Given Data / Assumptions:

• P = Rs. 576.
• BG = Re. 1.
• x = r * t unknown; simple interest applies.

Concept / Approach:
From P = F / (1 + x) ⇒ F = P * (1 + x). Then BG = F * x^2 / (1 + x) = P * (1 + x) * x^2 / (1 + x) = P * x^2. Thus x^2 = BG / P ⇒ x directly.

Step-by-Step Solution:
x^2 = BG / P = 1 / 576 ⇒ x = 1/24 (positive branch).F = P * (1 + x) = 576 * (1 + 1/24) = 576 * (25/24) = 600.TD = F − P = 600 − 576 = Rs. 24.

Verification / Alternative check:
TD also equals F * x / (1 + x) = 600 * (1/24) / (25/24) = 600 / 25 = 24, consistent.

Why Other Options Are Wrong:
16, 18, 32, 12 do not match once x = 1/24 is established.

Common Pitfalls:
Taking x = √(P / BG) instead of √(BG / P); forgetting F = P + TD.

Final Answer:
Rs. 24