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?

• A. 5 days
• B. 8 days
• C. 6 days
• D. 4 days

Hint:

Track the work completed in the first 2 days, then recompute the rate for the new team.

Answer 1

The Correct Option is A

Step 1: Assign a woman's daily work as 1 unit.
If one woman does 1 unit of work per day, one man, doing double, does 2 units per day. The original team of 8 men and 4 women then does $8(2)+4(1) = 16+4 = 20$ units per day.

Step 2: Work out the total job size and how much is left after 2 days.
Working 6 days at 20 units per day gives a total job of $20 \times 6 = 120$ units. After working for 2 days, $20 \times 2 = 40$ units are finished, leaving $120-40=80$ units.

Step 3: Recompute the daily rate for the new team.
Now only $8-4=4$ men and $4+4=8$ women are working, giving $4(2)+8(1) = 8+8=16$ units per day.

Final Answer:
The remaining 80 units at 16 units per day take $\frac{80}{16}=5$ more days to finish. \[ \boxed{5 \text{ days}} \]