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

Answer 1

The Correct Option is A

To solve this problem, we first need to determine the work rate of one man and one woman. Given: 8 men and 4 women can complete the work in 6 days. Let's denote the work done by one man in one day as m and by one woman in one day as w. We know:

1. m = 2w, since a man's work is double that of a woman.

2. Total work is completed in 6 days.

Therefore,
(8m + 4w) × 6 = Total work.

Substituting m = 2w, we have:
(8(2w) + 4w) × 6 = Total work
(16w + 4w) × 6 = Total work
20w × 6 = Total work
Total work = 120w.

Now, 8 men and 4 women work for 2 days:
(8m + 4w) × 2 days = Work done in 2 days
(16w + 4w) × 2 = Work done in 2 days
20w × 2 = 40w.

Remaining work = 120w - 40w = 80w.

After 2 days, 4 men leave and 4 new women join, resulting in 4 men and 8 women:
(4m + 8w) per day = Daily work rate
(8w + 8w) = 16w per day.

Remaining work is 80w. Therefore, time taken to complete the remaining work is:
80w ÷ 16w/day = 5 days.

Thus, in 5 more days, the work will be completed.

The correct answer is 5 days.