Banker’s Discount given (6 months @ 6%) → True Discount: The banker's discount on a bill due 6 months hence at 6% per annum is Rs. 37.08. What is the true discount?

Introduction / Context:
Banker's Discount (BD) is computed on the face value F: BD = F * r * t. True Discount (TD) discounts only to the present worth: TD = F * r * t / (1 + r * t). With BD known and r * t known, we can recover F and then TD.

Given Data / Assumptions:

• t = 6 months = 0.5 year; r = 6% ⇒ x = r * t = 0.06 * 0.5 = 0.03.
• BD = Rs. 37.08.

Concept / Approach:
Find F from BD = F * x ⇒ F = BD / x. Then TD = F * x / (1 + x) = BD / (1 + x).

Step-by-Step Solution:
F = 37.08 / 0.03 = Rs. 1236.TD = F * 0.03 / 1.03 = 37.08 / 1.03 = Rs. 36.00.

Verification / Alternative check:
BD − TD = BG = 37.08 − 36.00 = 1.08, which also equals F * x^2 / (1 + x) = 1236 * 0.0009 / 1.03 ≈ 1.08.

Why Other Options Are Wrong:
6.18, 12.36, 48, 37.80 don't match TD once x = 0.03 is applied; 48 corresponds to a different rate/time.

Common Pitfalls:
Forgetting to divide by (1 + x) when moving from BD to TD; mixing months and years.

Final Answer:
Rs. 36