The banker’s discount (BD) on a bill due 6 months hence at 6% p.a. is ₹37.08. Find the true discount (TD).

Introduction / Context:
Given BD and x = r * t, TD can be recovered via TD = BD / (1 + x). This identity follows directly from the relation BD = (1 + x) * TD in simple-interest bill discounting problems.

Given Data / Assumptions:

• BD = ₹37.08.
• t = 6 months = 0.5 year; r = 6% p.a. ⇒ x = 0.03.

Concept / Approach:
Compute TD = BD / (1 + x) = 37.08 / 1.03. Evaluate with care to avoid rounding errors.

Step-by-Step Solution:

Verification / Alternative check:
BG = BD − TD = 37.08 − 36 = ₹1.08. Also BG = x * TD = 0.03 * 36 = ₹1.08, consistent.

Why Other Options Are Wrong:
₹32 and ₹38 do not satisfy the exact division by 1.03; “None of these” is unnecessary since ₹36 fits perfectly.

Common Pitfalls:
Using months directly without conversion; rounding too early.

Final Answer:
Rs. 36