Find the true discount from banker’s gain and present worth: The present worth of a sum due sometime hence is ₹576 and the banker’s gain is ₹9. Determine the true discount.

Introduction / Context:
Banker’s Gain (BG) links to True Discount (TD) and r t via BG = TD * r t = PW * (r t)^2. Given PW and BG, we can find r t and then compute TD = PW * r t.

Given Data / Assumptions:

• PW = ₹576
• BG = ₹9

Concept / Approach:
Use:

Step-by-Step Solution:

Verification / Alternative check:
Since TD = PW * x = 72, BG should be TD * x = 72 * (1/8) = 9 (matches).

Why Other Options Are Wrong:
Other numbers do not satisfy the squared relation between BG, PW and x = r t.

Common Pitfalls:
Taking x as 9/576 instead of its square root, or mixing BD with BG/TD relations.

Final Answer:
₹ 72