The present worth (PW) of a sum due sometime hence is ₹576 and the banker’s gain (BG) is ₹1. Find the true discount (TD).

Introduction / Context:For simple-interest bill discounting, PW (present worth), TD (true discount), BD (banker’s discount), and BG (banker’s gain) are tightly related via the parameter x = r * t. With PW and BG given, TD can be computed directly using compact identities.

Given Data / Assumptions:

• PW = ₹576.
• BG = ₹1.
• All quantities based on simple interest conventions.

Concept / Approach:Let x = r * t. Then PW = F / (1 + x), TD = F * x / (1 + x) and BG = F * x^2 / (1 + x). Eliminating F gives TD = x * PW and BG = x^2 * PW. Hence x = sqrt(BG / PW) and then TD = x * PW = sqrt(BG * PW).

Step-by-Step Solution:

Verification / Alternative check:Compute BG from x and PW: BG = x^2 * PW = (1/24)^2 * 576 = (1/576) * 576 = ₹1, matches.

Why Other Options Are Wrong:₹16, ₹18, and ₹32 do not satisfy the identity TD = sqrt(BG * PW) with BG = 1 and PW = 576.

Common Pitfalls:Attempting to find r or t separately; the problem only needs the combined factor via x.

Final Answer:Rs. 24