The true discount (TD) on a bill of ₹2160 is ₹360. Compute the banker’s discount (BD).

Introduction / Context:
True discount and face value are known; we must find BD. Use the identity TD = F * x / (1 + x) to find x, then use BD = F * x or BD = (1 + x) * TD. This avoids needing r or t individually.

Given Data / Assumptions:

• F = ₹2160.
• TD = ₹360.

Concept / Approach:
Let x = r * t. Then 360 = 2160 * x / (1 + x). Solve for x, then BD = 2160 * x.

Step-by-Step Solution:

Verification / Alternative check:
Also BD = (1 + x) * TD = 1.2 * 360 = ₹432, same result.

Why Other Options Are Wrong:
Values like 412, 422, 442 do not satisfy both TD and the derived x.

Common Pitfalls:
Using BD = TD / (1 + x) (incorrect direction); BD is larger than TD for x > 0.

Final Answer:
Rs. 432