A bill is due 4 months hence at 15% p.a. The banker’s discount (BD) is ₹420. Find the true discount (TD).
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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ARs. 410
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BRs. 400
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CRs. 390
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DRs. 380
Answer
Correct Answer: Rs. 400
Explanation
Introduction / Context:When BD and x = r * t are known, TD follows from TD = BD / (1 + x). This is because BD = (1 + x) * TD under simple-interest bill discounting.
Given Data / Assumptions:
- BD = ₹420.
- t = 4 months = 1/3 year; r = 15% p.a.
Concept / Approach:Compute x = r * t; then TD = BD / (1 + x). No need to compute the face value explicitly.
Step-by-Step Solution:
x = 0.15 * (1/3) = 0.05.TD = BD / (1 + x) = 420 / 1.05 = ₹400.Verification / Alternative check:BG = BD − TD = 420 − 400 = ₹20. Also BG = x * TD = 0.05 * 400 = ₹20, matches.
Why Other Options Are Wrong:₹380, ₹390, and ₹410 are off the exact ratio division by 1.05.
Common Pitfalls:Using months directly without converting to years; confusing TD with PW.
Final Answer:Rs. 400