The true discount (TD) on a bill of ₹2160 is ₹360. Compute the banker’s discount (BD).
Aptitude
Banker's Discount
Difficulty: Medium
Choose an option
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ARs. 432
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BRs. 422
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CRs. 412
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DRs. 442
Answer
Correct Answer: Rs. 432
Explanation
Introduction / Context:True discount and face value are known; we must find BD. Use the identity TD = F * x / (1 + x) to find x, then use BD = F * x or BD = (1 + x) * TD. This avoids needing r or t individually.
Given Data / Assumptions:
- F = ₹2160.
- TD = ₹360.
Concept / Approach:Let x = r * t. Then 360 = 2160 * x / (1 + x). Solve for x, then BD = 2160 * x.
Step-by-Step Solution:
360(1 + x) = 2160x ⇒ 360 = 2160x − 360x = 1800x ⇒ x = 0.2.BD = F * x = 2160 * 0.2 = ₹432.Verification / Alternative check:Also BD = (1 + x) * TD = 1.2 * 360 = ₹432, same result.
Why Other Options Are Wrong:Values like 412, 422, 442 do not satisfy both TD and the derived x.
Common Pitfalls:Using BD = TD / (1 + x) (incorrect direction); BD is larger than TD for x > 0.
Final Answer:Rs. 432