In how many days can 4 women complete a work?
I. 4 men and 4 women can complete the same work in 12 days.
II. 10 women can complete the same work in 16 days

Options

A. If statement I alone is sufficient but statement II alone is not sufficient.
B. If statement Il alone is sufficient but statement I alone is not sufficient.
C. If each statement alone (either I or II) is sufficient.
D. If statement and Il together are not sufficient

Answer

To solve the problem of how many days 4 women can complete a work, we will analyze the two statements provided and derive the necessary information step by step.

### Step 1: Analyze Statement II
The second statement tells us that 10 women can complete the work in 16 days.

**Calculation:**
- If 10 women can complete the work in 16 days, we can find out how much work one woman can do in one day.
- Total work done by 10 women in 16 days = 10 women * 16 days = 160 woman-days of work.
- Therefore, 1 woman can complete the work in \( \frac{160}{10} = 16 \) days.

### Step 2: Calculate Work Done by 4 Women
Now that we know how long it takes for one woman to complete the work, we can find out how long it takes for 4 women to complete the same work.

**Calculation:**
- If 1 woman takes 160 days to complete the work, then 4 women will take:
\[ \text{Time taken by 4 women} = \frac{160 \text{ days}}{4} = 40 \text{ days} \]

### Conclusion
Thus, 4 women can complete the work in **40 days**.