Find banker’s discount from banker’s gain: The banker’s gain on a sum due 3 years hence at 12% per annum is ₹360. Compute the banker’s discount.
Aptitude
Banker's Discount
Difficulty: Medium
Choose an option
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ARs. 1360
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BRs. 1000
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CRs. 360
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DRs. 640
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ENone of these
Answer
Correct Answer: Rs. 1360
Explanation
Introduction / Context:From BG and r t we can find the face value A, and then compute BD = A * r t. This question emphasizes the utility of the BG identity in reverse.
Given Data / Assumptions:t = 3 years; r = 12% ⇒ r t = 0.36; BG = ₹360.
Concept / Approach:
BG = A * (r t)^2 / (1 + r t) ⇒ A = BG * (1 + r t) / (r t)^2 Then BD = A * r tStep-by-Step Solution:
A = 360 * 1.36 / (0.36)^2 = 360 * 1.36 / 0.1296 = ₹3777.78 BD = A * 0.36 ≈ 3777.78 * 0.36 = ₹1360Verification / Alternative check:TD = BD − BG ≈ 1360 − 360 = ₹1000; TD should also equal A * 0.36 / 1.36 ≈ 1000 (checks).
Final Answer:Rs. 1360