A work could be completed by certain workers in 22 days. However, due to 3…
2024
A work could be completed by certain workers in 22 days. However, due to 3 workers being absent, it was completed in 24 days. The original number of workers was –
Answer: C. 36 — Concept: When a fixed job is done by equally-efficient workers, the total work stays constant and equals the number of workers multiplied by the number of…
- A.
38
- B.
42
- C.
36
- D.
45
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Correct answer: C
Concept: When a fixed job is done by equally-efficient workers, the total work stays constant and equals the number of workers multiplied by the number of days taken. So for the same job done by two different-sized crews: Workers1 × Days1 = Workers2 × Days2.
Let x be the original number of workers, who complete the job in 22 days.
With 3 workers absent, only (x − 3) workers complete the same job, taking 24 days instead.
Since the total work is the same in both cases, equate workers × days: x × 22 = (x − 3) × 24.
Expand the right-hand side: 22x = 24x − 72.
Collect the x terms on one side: 24x − 22x = 72, so 2x = 72.
Divide both sides by 2: x = 36.
Cross-check: 36 workers × 22 days = 792 units of work. With 3 workers absent, 33 workers × 24 days = 792 units of work — the same total, confirming the original number of workers was 36.