Explanation:

- We are given two scenarios:

- "Two men and 7 women can complete a work in 28 days."

- "Six men and 16 women can do the same work in 11 days."

- We need to find out how many days 7 men alone will take to complete the same work.

- First, let's find the total work in terms of man-days and woman-days.

- Let M be the work a man does in one day, and W be the work a woman does in one day.

- From the first statement:

$$28\times (2M+7W)=W$$

- From the second statement:

$$11\times (6M+16W)=W$$

- Solving these linear equations will give us the individual work rates of men and women.

- Once we find M, we can use it to find how many days 7 men would take:

$$Days=\frac{TotalWork}{7M}$$

- Performing these calculations accurately will lead to the right option that represents the number of days 7 men will need.

- Answer: Option 3, 12 days