Question:
8 men and 4 women together can complete a piece of work in 6 days. The work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days 4 men left and 4 new women joined, in how many more days will the work be completed?
8 men and 4 women together can complete a piece of work in 6 days. The work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days 4 men left and 4 new women joined, in how many more days will the work be completed?
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Track the work completed in the first 2 days, then recompute the rate for the new team.
Updated On: Jul 16, 2026
- 5 days
- 8 days
- 6 days
- 4 days
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Set up daily work rates.
Let the work done by one woman in a day be \(x\) units, so one man does \(2x\) units in a day (double a woman's work). With 8 men and 4 women working together, the daily work rate is \(8(2x)+4x = 16x+4x = 20x\) units per day.
Step 2: Find the total work and the work done in the first 2 days.
Since this team finishes the job in 6 days, total work \(=20x \times 6 = 120x\) units. In the first 2 days, the team completes \(20x \times 2 = 40x\) units, leaving \(120x-40x=80x\) units still to be done.
Step 3: Find the new daily rate after the change in team.
After 2 days, 4 men leave (8-4=4 men remain) and 4 new women join (4+4=8 women). The new daily rate is \(4(2x)+8x = 8x+8x=16x\) units per day.
Final Answer:
Time to finish the remaining 80x units at 16x units per day is \(\frac{80x}{16x}=5\) days. \[ \boxed{5 \text{ days}} \]
Let the work done by one woman in a day be \(x\) units, so one man does \(2x\) units in a day (double a woman's work). With 8 men and 4 women working together, the daily work rate is \(8(2x)+4x = 16x+4x = 20x\) units per day.
Step 2: Find the total work and the work done in the first 2 days.
Since this team finishes the job in 6 days, total work \(=20x \times 6 = 120x\) units. In the first 2 days, the team completes \(20x \times 2 = 40x\) units, leaving \(120x-40x=80x\) units still to be done.
Step 3: Find the new daily rate after the change in team.
After 2 days, 4 men leave (8-4=4 men remain) and 4 new women join (4+4=8 women). The new daily rate is \(4(2x)+8x = 8x+8x=16x\) units per day.
Final Answer:
Time to finish the remaining 80x units at 16x units per day is \(\frac{80x}{16x}=5\) days. \[ \boxed{5 \text{ days}} \]
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