The present worth (PW) of a sum due sometime hence is ₹5760 and the banker’s gain (BG) is ₹10. Compute the true discount (TD).

Introduction / Context:
Given PW and BG, the true discount can be obtained without knowing the face value or the rate/time individually, by employing identities in x = r * t.

Given Data / Assumptions:

• PW = ₹5760.
• BG = ₹10.

Concept / Approach:
Key relations: TD = x * PW and BG = x^2 * PW. Hence x = sqrt(BG / PW), and TD = x * PW = sqrt(BG * PW). This is the fastest computation path here.

Step-by-Step Solution:

Verification / Alternative check:
BG = x * TD = (TD / PW) * TD = TD^2 / PW = 240^2 / 5760 = 57600 / 5760 = ₹10, checks out.

Why Other Options Are Wrong:
₹120, ₹420, and ₹480 do not satisfy TD = sqrt(BG * PW) with the given values.

Common Pitfalls:
Trying to determine rate or time separately; it is unnecessary here.

Final Answer:
Rs. 240