The true discount (TD) on a bill of ₹1860 due after 8 months is ₹60. Find the banker’s gain (BG).
Aptitude
Banker's Discount
Difficulty: Medium
Choose an option
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ARs. 1.5
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BRs. 2.5
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CRs. 4
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DRs. 2
Answer
Correct Answer: Rs. 2
Explanation
Introduction / Context:We are given TD and face value F; the time (8 months) is mentioned but rate is not. However, we can find x = r * t directly from TD and F: TD = F * x / (1 + x). Having x, BG = x * TD. No need to split x into r and t separately.
Given Data / Assumptions:
- F = ₹1860.
- TD = ₹60.
Concept / Approach:Solve TD = F * x / (1 + x) for x, then compute BG = x * TD. This is efficient and general.
Step-by-Step Solution:
60(1 + x) = 1860x ⇒ 60 = 1860x − 60x = 1800x ⇒ x = 1/30.BG = x * TD = (1/30) * 60 = ₹2.Verification / Alternative check:BD = (1 + x)*TD = (31/30)*60 = ₹62; BG = BD − TD = 62 − 60 = ₹2, consistent.
Why Other Options Are Wrong:₹1.5, ₹2.5, ₹4 do not equal x * TD with x = 1/30.
Common Pitfalls:Attempting to find r explicitly; not required because BG depends on x only.
Final Answer:Rs. 2