8 men and 4 woment together can complete a piece ot work in 6 days. Work done by a man in one day is double the work done by a women in one day 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined the work.
Quantity I: more days required to complete the work
II: 5 days

Options

A. Quantity `I=` Quantity II or No relation
B. Quantity `Ige` Quantity II
C. Quantity `I lt` Quantity II
D. Quantity `I le Quantity II

Explanation

To solve the problem step by step, we need to analyze the work done by men and women, and how the workforce changes over time.

### Step 1: Calculate the total work done by 8 men and 4 women in 6 days.

Given that:
- 8 men and 4 women can complete the work in 6 days.
- The work done by a man in one day is double that of a woman.

Let the work done by one woman in one day be \( W \). Then, the work done by one man in one day is \( 2W \).

Thus, the total work done by 8 men and 4 women in one day is:
\[ \text{Total work in one day} = 8 \times 2W + 4 \times W = 16W + 4W = 20W \]

In 6 days, the total work done is:
\[ \text{Total work} = 20W \times 6 = 120W \]

### Step 2: Calculate the work done in the first 2 days.

In 2 days, the total work done by 8 men and 4 women is:
\[ \text{Work done in 2 days} = 20W \times 2 = 40W \]

### Step 3: Calculate the remaining work.

The remaining work after 2 days is:
\[ \text{Remaining work} = 120W - 40W = 80W \]

### Step 4: Analyze the change in workforce.

After 2 days, 4 men leave, and 4 new women join.

- The remaining workforce consists of:
- 4 men (since 8 - 4 = 4)
- 8 women (since 4 + 4 = 8)

The total work done by the new workforce in one day is:
\[ \text{Work done by 4 men and 8 women} = 4 \times 2W + 8 \times W = 8W + 8W = 16W \]

### Step 5: Calculate the number of days required to complete the remaining work.

To find out how many days are required to complete the remaining work of \( 80W \) with the new workforce:
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Work done per day}} = \frac{80W}{16W} = 5 \text{ days} \]

### Step 6: Compare the quantities.

- Quantity I: More days required to complete the work = 5 days
- Quantity II: 5 days

### Conclusion:

Both quantities are equal. Therefore, the answer is that Quantity I is equal to Quantity II.

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