In how many days 10 women can finish the work
I. 10 men finish the work in 6 days.
II. 10 women and 10 men finish the work in `3(3)/(7)` days.
III. If 10 men work 3 days and after that 10 women are deployed to work for men, the rest work is finighed in 4 days. (a) I and II (b) Any two of three (c) I and III (d) II and III

Options

A. I and II
B. Any two of three
C. I and III
D. II and III

Explanation

To determine how many days 10 women can finish the work, we will analyze the given statements step by step.

### Step 1: Analyze Statement I
Statement I states that "10 men finish the work in 6 days."

- If 10 men can complete the work in 6 days, then the total work can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Days} = 10 \text{ men} \times 6 \text{ days} = 60 \text{ man-days} \]

### Step 2: Analyze Statement II
Statement II states that "10 women and 10 men finish the work in \(3 \frac{3}{7}\) days."

- First, convert \(3 \frac{3}{7}\) days into an improper fraction:
\[ 3 \frac{3}{7} = \frac{24}{7} \text{ days} \]
- The total work done by 10 men and 10 women in this time is:
\[ \text{Total Work} = (\text{Number of Men} + \text{Number of Women}) \times \text{Days} = (10 + 10) \times \frac{24}{7} = 20 \times \frac{24}{7} = \frac{480}{7} \text{ man-woman days} \]

### Step 3: Analyze Statement III
Statement III states that "If 10 men work for 3 days and then 10 women are deployed to finish the rest of the work in 4 days."

- The work done by 10 men in 3 days:
\[ \text{Work done by Men} = 10 \text{ men} \times 3 \text{ days} = 30 \text{ man-days} \]
- The remaining work is:
\[ \text{Remaining Work} = 60 \text{ man-days} - 30 \text{ man-days} = 30 \text{ man-days} \]
- If 10 women finish this remaining work in 4 days, then:
\[ \text{Work done by Women} = 10 \text{ women} \times 4 \text{ days} = 40 \text{ woman-days} \]
- This means that the total work can also be expressed as:
\[ 30 \text{ man-days} = 40 \text{ woman-days} \]

### Step 4: Calculate the Efficiency of Women
From Statement III, we can find the efficiency of women in terms of men:
- Since 30 man-days = 40 woman-days, we can find the efficiency of 1 woman in terms of men:
\[ \frac{30}{40} = \frac{3}{4} \text{ man-days per woman} \]
- Therefore, 10 women can do:
\[ 10 \text{ women} \times \frac{3}{4} \text{ man-days per woman} = 7.5 \text{ man-days} \]

### Step 5: Calculate Days Taken by 10 Women to Finish the Work
To find out how many days 10 women take to finish the total work of 60 man-days:
- If 10 women do 7.5 man-days of work in 1 day, then:
\[ \text{Days taken by 10 women} = \frac{60 \text{ man-days}}{7.5 \text{ man-days per day}} = 8 \text{ days} \]

### Conclusion
From the analysis of the statements, we can conclude that both Statements II and III are sufficient to determine how many days 10 women can finish the work.

### Final Answer
The correct option is (d) II and III.

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