The true discount (TD) on a bill of ₹540 is ₹90. Compute the banker’s discount (BD).

Introduction / Context:
Face value F and TD are known; we can find x from TD = F * x / (1 + x) and then compute BD via BD = F * x or BD = (1 + x) * TD. This is a straightforward algebraic step.

Given Data / Assumptions:

• F = ₹540.
• TD = ₹90.

Concept / Approach:
Use the TD identity to solve for x, then compute BD = F * x. This avoids finding r and t separately.

Step-by-Step Solution:

Verification / Alternative check:
BD = (1 + x)*TD = 1.2 * 90 = ₹108; consistent.

Why Other Options Are Wrong:
₹60, ₹110, ₹150 do not satisfy the derived x = 0.2 simultaneously with TD = 90.

Common Pitfalls:
Confusing TD and BD or forgetting that BD exceeds TD by BG = x * TD for x > 0.

Final Answer:
Rs. 108