On a certain sum, the banker’s discount (BD) is ₹36 and the true discount (TD) is ₹30 for the same time and rate. What is the sum due (face value F)?
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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ARs. 180
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BRs. 120
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CRs. 220
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DRs. 200
Answer
Correct Answer: Rs. 180
Explanation
Introduction / Context:Given BD and TD only, we can extract x = r * t using BD/TD, then use BD = F * x to compute the face value F directly. This avoids explicit rate/time values.
Given Data / Assumptions:
- BD = ₹36.
- TD = ₹30.
Concept / Approach:Identity: BD/TD = 1 + x ⇒ x = BD/TD − 1 = 36/30 − 1 = 1/5. Then BD = F * x ⇒ F = BD / x.
Step-by-Step Solution:
x = (36/30) − 1 = 6/5 − 1 = 1/5 = 0.2.F = BD / x = 36 / 0.2 = ₹180.Verification / Alternative check:TD = F * x / (1 + x) = 180 * 0.2 / 1.2 = 36 / 1.2 = ₹30, matches.
Why Other Options Are Wrong:₹120, ₹200, ₹220 do not satisfy both BD and TD under the same x.
Common Pitfalls:Using TD = F * x (incorrect); TD is discounted by 1 + x in the denominator.
Final Answer:Rs. 180