The true discount (TD) on a bill of ₹540 is ₹90. Compute the banker’s discount (BD).
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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ARs. 60
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BRs. 150
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CRs. 108
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DRs. 110
Answer
Correct Answer: Rs. 108
Explanation
Introduction / Context:Face value F and TD are known; we can find x from TD = F * x / (1 + x) and then compute BD via BD = F * x or BD = (1 + x) * TD. This is a straightforward algebraic step.
Given Data / Assumptions:
- F = ₹540.
- TD = ₹90.
Concept / Approach:Use the TD identity to solve for x, then compute BD = F * x. This avoids finding r and t separately.
Step-by-Step Solution:
90(1 + x) = 540x ⇒ 90 = 450x ⇒ x = 0.2.BD = F * x = 540 * 0.2 = ₹108.Verification / Alternative check:BD = (1 + x)*TD = 1.2 * 90 = ₹108; consistent.
Why Other Options Are Wrong:₹60, ₹110, ₹150 do not satisfy the derived x = 0.2 simultaneously with TD = 90.
Common Pitfalls:Confusing TD and BD or forgetting that BD exceeds TD by BG = x * TD for x > 0.
Final Answer:Rs. 108