2 children = 1 man(8 children + 12 men ) = 16 menNow, less men, more days12 : 16 : 9 : xx = 16�9/12=12 days

Solution:

Let's break down the problem into smaller parts and solve them step by step.

Step 1: Understand the given information
- There are 8 men and 2 children.
- They can complete a work in 9 days.
- A child takes double the time to do a work than a man.

Step 2: Calculate the work rate
Let the work rate of a man be M units per day.
So, the work rate of a child will be 2M units per day as a child takes double the time to complete the same work.

The total work to be done is given by:
Work = (8 men + 2 children) x (9 days) x (M units/day)
= 72M units

Step 3: Calculate the work rate of a man
Since the total work is 72M units and it takes 9 days for 8 men and 2 children to complete it, we can calculate the work rate of a man per day as follows:
Work rate of a man = Total work / (Number of days x Number of men)
= 72M / (9 x 8)
= M units/day

Step 4: Calculate the work rate of a child
As given, a child takes double the time to complete the same work as a man. Therefore, the work rate of a child per day can be calculated as:
Work rate of a child = 2M units/day

Step 5: Calculate the total work to be done by 12 men
We need to find the number of days required for 12 men to complete double the work. Let's calculate the total work to be done by 12 men:
Total work = (12 men) x (Number of days) x (Work rate of a man)
= 12M units/day x Number of days

We know that the total work to be done is double the initial work, which is 72M units. So we can write the equation as:
12M units/day x Number of days = 2 x 72M units

Step 6: Solve for the number of days
Simplifying the equation from step 5, we get:
Number of days = (2 x 72M units) / (12M units/day)
= 144M units / (12M units/day)
= 12 days

Step 7: Conclusion
Therefore, 12 men can complete double the work in 12 days.

Summary:
- Given 8 men and 2 children can complete a work in 9 days.
- A child takes double the time to do a work than a man.
- We calculated the work rates of a man and a child.
- Using the work rates, we found the total work to be done and the work rate of a man.
- Then, we calculated the total work to be done by 12 men.
- Finally, we solved for the number of days required for 12 men to complete double the work, which is 12 days.