8 children and 12 men complete a certain piece of work in 9 days Each child takes twice the time taken by a man to finish the work In how many days will 12 men finish the same work?

13.5 days

Rate of work for men = m

Rate of work for children = c

Therefore if we combine the rates:

m + c = 1/9

Since rate = work-done/time

Now m = 2c since rate of men is twice the rate of children

Similarly, c = m/2 (rearranging the above)

Equation becomes:

m + m/2 = 1/9

3m/2 = 1/9

3m = 2/9

m = 2/27

This is the rate at which men work.

For the men to complete the work, it will take x days.

Rate = work/time

Rate = work/x

Work is 1

Rate is 2/27

2/27 = 1/x

x = 27/2

x = 13.5