Find TD and BG from given BD: The banker’s discount on ₹1650 due a certain time hence is ₹165. Determine the true discount and the banker’s gain.
Aptitude
Banker's Discount
Difficulty: Easy
Choose an option
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ARs. 150, Rs. 15
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BRs. 160, Rs. 5
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CRs. 145, Rs. 20
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DNone of these
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E—
Answer
Correct Answer: Rs. 150, Rs. 15
Explanation
Introduction / Context:Knowing BD on a face amount directly gives r t because BD = A * r * t. Once r t is known, TD and BG follow immediately.
Given Data / Assumptions:
- A = ₹1650
- BD = ₹165
Concept / Approach:
BD = A * r * t ⇒ r t = BD / A = 165 / 1650 = 0.10 TD = A * (r t) / (1 + r t) BG = BD − TDStep-by-Step Solution:
TD = 1650 * 0.10 / 1.10 = ₹150 BG = 165 − 150 = ₹15Verification / Alternative check:PW = A − TD = 1650 − 150 = ₹1500; interest on PW at r t = 0.10 equals ₹150 (the TD), confirming consistency.
Why Other Options Are Wrong:They do not reflect r t = 0.10 implied by BD/A = 0.10.
Common Pitfalls:Confusing TD with BD or computing TD without dividing by (1 + r t).
Final Answer:Rs. 150, Rs. 15