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)?
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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A₹ 15
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B₹ 20
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C₹ 25
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D₹ 5
Answer
Correct Answer: ₹ 20
Explanation
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:
x = 0.05.TD = BG / x = 1 / 0.05 = ₹20.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