Find BD when TD on a Rs 540 bill is Rs 90: On a bill of Rs 540, the true discount is Rs 90. What is the banker’s discount (for the same term and rate)?

Introduction / Context:
Given TD and face value S, we can infer x = r * t using PW or directly via TD = PW * x and PW = S − TD.

Given Data / Assumptions:
S = 540; TD = 90.

Concept / Approach:
PW = S − TD = 540 − 90 = 450. Then x = TD / PW = 90 / 450 = 0.2. BD = S * x.

Step-by-Step Solution:

Verification / Alternative check:
TD = BD / (1 + x) = 108 / 1.2 = 90 ✔️.

Why Other Options Are Wrong:
120, 102, 106 do not satisfy the needed ratio with TD = 90.

Common Pitfalls:
Taking BD = TD; forgetting to compute PW first.

Final Answer:
Rs 108