Compute banker’s discount and banker’s gain: The present worth of a bill is ₹2200 and the true discount is ₹220. Find the banker’s discount and the banker’s gain.
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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ABG = ₹ 22 and BD = ₹ 242
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BBG = ₹ 242 and BD = ₹ 22
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CBG = ₹ 11 and BD = ₹ 121
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DBG = ₹ 31 and BD = ₹ 343
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ENone of these
Answer
Correct Answer: BG = ₹ 22 and BD = ₹ 242
Explanation
Introduction / Context:From present worth (PW) and true discount (TD) we can find face value and r t. Then BD and BG follow mechanically. A key identity: TD / PW = r t.
Given Data / Assumptions:
- PW = ₹2200
- TD = ₹220
- A = PW + TD = ₹2420
Concept / Approach:Use:
r t = TD / PW BD = A * r * t BG = BD − TDStep-by-Step Solution:
r t = 220 / 2200 = 0.10 BD = 2420 * 0.10 = ₹242 BG = BD − TD = 242 − 220 = ₹22Verification / Alternative check:TD = A * (r t) / (1 + r t) = 2420 * 0.10 / 1.10 = ₹220 (checks).
Why Other Options Are Wrong:They mis-order BG and BD magnitudes or break the relation TD/PW = r t = 0.10.
Common Pitfalls:Using face value instead of PW when computing r t from TD, or swapping BG and BD definitions.
Final Answer:BG = ₹ 22 and BD = ₹ 242