Find time when BD(1600 at 15%) equals TD(1680 at 15%) for same term: The banker’s discount on Rs 1600 at 15% p.a. equals the true discount on Rs 1680 for the same time and rate. Find the time.
Aptitude
Banker's Discount
Difficulty: Medium
Choose an option
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A3 months
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B4 months
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C5 months
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D6 months
Answer
Correct Answer: 4 months
Explanation
Introduction / Context:Use BD = S1 * r * t and TD = S2 * r * t / (1 + r * t). Given BD(1600) = TD(1680), solve for t.
Given Data / Assumptions:S1 = 1600; S2 = 1680; r = 15% p.a.; t = ?
Concept / Approach:1600 * r * t = 1680 * r * t / (1 + r t) → 1600(1 + r t) = 1680 → 1 + r t = 1680/1600 = 1.05 → r t = 0.05.
Step-by-Step Solution:
r = 0.15 → t = 0.05 / 0.15 = 1/3 year = 4 months.Verification / Alternative check:Check equality numerically at t = 1/3 year; both sides match.
Why Other Options Are Wrong:3, 5, 6 months do not satisfy 1 + r t = 1.05.
Common Pitfalls:Canceling t improperly; forgetting both sides share r * t.
Final Answer:4 months