True Discount given (16 months) → Banker’s Gain: The true discount on a bill of ₹ 7440 due 16 months hence is ₹ 240. Find the banker's gain.
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A₹ 10
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B₹ 6
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C₹ 4
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D₹ 8
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E₹ 12
Answer
Correct Answer: ₹ 8
Explanation
Introduction / Context:Once TD is given, we can solve for x = r * t using TD = F * x / (1 + x). Banker's Discount is BD = F * x, and Banker's Gain is BG = BD − TD.
Given Data / Assumptions:
- F = ₹ 7440.
- t = 16 months = 16/12 years = 4/3 years.
- TD = ₹ 240.
Concept / Approach:Let x = r * t. Solve for x from the TD equation, then compute BD and BG.
Step-by-Step Solution:TD = 7440 x / (1 + x) = 240 ⇒ 7440 x = 240 + 240 x ⇒ 7200 x = 240 ⇒ x = 1/30.BD = 7440 * (1/30) = ₹ 248.BG = BD − TD = 248 − 240 = ₹ 8.
Verification / Alternative check:P = F − TD = 7440 − 240 = 7200; also P = F / (1 + x) = 7440 / (31/30) = 7200, consistent.
Why Other Options Are Wrong:10, 6, 4, 12 do not match BG once x = 1/30 is established.
Common Pitfalls:Arithmetic slips when isolating x; forgetting BG = BD − TD.
Final Answer:₹ 8