A bill is due 1 year hence at 5% simple interest. The banker’s gain (BG) is Re. 1. What is the true discount (TD)?

Introduction / Context:
Here the period and rate are known, so x = r * t is known. A direct identity links banker’s gain (BG) and true discount (TD): BG = x * TD. We can compute TD from BG and x immediately.

Given Data / Assumptions:

• t = 1 year, r = 5% p.a.
• BG = Re. 1.
• Simple-interest bill-discounting framework applies.

Concept / Approach:
Let x = r * t = 0.05 * 1 = 0.05. Using identities: TD = F * x / (1 + x) and BG = F * x^2 / (1 + x). Dividing gives BG = x * TD ⇒ TD = BG / x.

Step-by-Step Solution:

Verification / Alternative check:
If TD = ₹20, BG should be x * TD = 0.05 * 20 = Re. 1, consistent.

Why Other Options Are Wrong:
₹5, ₹15, and ₹25 violate BG = x * TD with x = 0.05.

Common Pitfalls:
Confusing TD with BD; note BD = (1 + x) * TD, not needed here because BG gives TD directly.

Final Answer:
₹ 20