Given banker’s gain, find present worth: The banker’s gain on a sum due 3 years hence at 10% per annum is Rs 36. Find the present worth (PW).
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ARs. 400
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BRs. 300
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CRs. 500
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DRs. 350
Answer
Correct Answer: Rs. 400
Explanation
Introduction / Context:Banker’s gain (BG) equals BD − TD and also equals S * r^2 * t^2 / (1 + r t). From BG we can find the face value S and then the present worth PW = S / (1 + r t).
Given Data / Assumptions:
- BG = Rs 36, r = 10% p.a., t = 3 years.
Concept / Approach:Use BG = S * r^2 * t^2 / (1 + r t). Compute S, then PW = S / (1 + r t). Here r t = 0.3 and r^2 t^2 = 0.09.
Step-by-Step Solution:
36 = S * 0.09 / 1.3 → S = 36 * 1.3 / 0.09 = 520.PW = S / (1 + r t) = 520 / 1.3 = Rs 400.Verification / Alternative check:BD = S * r * t = 520 * 0.3 = 156; TD = BD / (1 + r t) = 156 / 1.3 = 120; BG = 156 − 120 = 36 ✔️; PW = 520 / 1.3 = 400 ✔️.
Why Other Options Are Wrong:300, 500, 350 do not make BD − TD equal to 36 at 10% for 3 years.
Common Pitfalls:Using compound interest; forgetting to divide by (1 + r t) when moving from S to PW.
Final Answer:Rs 400