Two-worker payment from rates: A completes a job in 3 days, B in 4 days. They work together and receive ₹ 2800 in total. How much should A receive, if the split is proportional to work done?
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A₹ 1600
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B₹ 1900
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C₹ 1200
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D₹ 1300
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E₹ 1400
Answer
Correct Answer: ₹ 1600
Explanation
Introduction / Context: A and B have constant daily rates inversely proportional to their completion times. When they complete the job together, the fair split of wages is proportional to their rates, since both contributed for the same duration to finish the job once.
Given Data / Assumptions:
- A: 3 days ⇒ rate = 1/3.
- B: 4 days ⇒ rate = 1/4.
- Total payment = ₹ 2800.
Concept / Approach: Split by rates: A : B = 1/3 : 1/4. Convert to a simple integer ratio and apply it to the total payment to find A’s share precisely.
Step-by-Step Solution:
A : B = 1/3 : 1/4 = 4 : 3.Total parts = 4 + 3 = 7.A’s share = 4/7 * 2800 = ₹ 1600.Verification / Alternative check: B’s share = 3/7 * 2800 = ₹ 1200; sums to ₹ 2800 and matches the 4:3 rate ratio.
Why Other Options Are Wrong: ₹ 1900, ₹ 1300, ₹ 1400, and ₹ 1200 do not reflect the 4/7 fraction for A.
Common Pitfalls: Averaging days or wages instead of using the correct reciprocal relationship of days and rates.
Final Answer: ₹ 1600