8 men and 5 women together can complete a piece of work in 7 days and work done by a women in one day is half the work done by a man in one day. If 9 men and 3 women started working and after 4 days 4 men left the work and 4 new women joined then, in how many many more days will the work be completed

Options

A. 7 days
B. 6 days
C. 5.25 days
D. 3.7 days

Explanation

To solve the problem step by step, let's break it down systematically.

### Step 1: Determine the work done by men and women
Let the work done by one woman in one day be \( w \). Therefore, the work done by one man in one day will be \( 2w \) (since a woman does half the work of a man).

### Step 2: Calculate total work done by 8 men and 5 women in 7 days
The total work done by 8 men and 5 women in one day can be calculated as follows:
- Work done by 8 men in one day: \( 8 \times 2w = 16w \)
- Work done by 5 women in one day: \( 5 \times w = 5w \)

Thus, the total work done in one day by 8 men and 5 women is:
\[ 16w + 5w = 21w \]

Since they complete the work in 7 days, the total work \( W \) can be calculated as:
\[ W = \text{(Work done in one day)} \times \text{(Number of days)} = 21w \times 7 = 147w \]

### Step 3: Calculate work done by 9 men and 3 women in 4 days
Now, 9 men and 3 women start working for 4 days. The work done in one day by 9 men and 3 women is:
- Work done by 9 men in one day: \( 9 \times 2w = 18w \)
- Work done by 3 women in one day: \( 3 \times w = 3w \)

Thus, the total work done in one day by 9 men and 3 women is:
\[ 18w + 3w = 21w \]

The work done in 4 days is:
\[ \text{Work done in 4 days} = 21w \times 4 = 84w \]

### Step 4: Calculate remaining work after 4 days
The remaining work after 4 days is:
\[ \text{Remaining work} = \text{Total work} - \text{Work done in 4 days} = 147w - 84w = 63w \]

### Step 5: Calculate the new work team after changes
After 4 days, 4 men leave and 4 new women join. The new team consists of:
- Remaining men: \( 9 - 4 = 5 \)
- Total women now: \( 3 + 4 = 7 \)

The work done in one day by the new team is:
- Work done by 5 men in one day: \( 5 \times 2w = 10w \)
- Work done by 7 women in one day: \( 7 \times w = 7w \)

Thus, the total work done in one day by the new team is:
\[ 10w + 7w = 17w \]

### Step 6: Calculate the number of days to complete the remaining work
To find out how many more days are needed to complete the remaining work of \( 63w \):
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Work done in one day}} = \frac{63w}{17w} = \frac{63}{17} \approx 3.71 \text{ days} \]

### Final Answer
Thus, the work will be completed in approximately **3.71 days**.

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