If 40 men or 60 women or 80 children can do a piece of work in 6 months, then 10 men, 10 women and 10 children together do half of the work in ?

First, we need to find the work done by one man, one woman, and one child in one day.

Given that 40 men can do the work in 6 months (or 180 days), the work done by one man in one day is 1/(40*180).

Similarly, the work done by one woman in one day is 1/(60180), and the work done by one child in one day is 1/(80180).

Now, if 10 men, 10 women, and 10 children work together, the work done in one day is 10/(40180) + 10/(60180) + 10/(80*180).

To find out how long it will take them to do half the work, we divide 0.5 (half the work) by the work done in one day.

So, the time taken to do half the work is 0.5 / (10/(40180) + 10/(60180) + 10/(80*180)).

After simplifying this, we find that it will take approximately 60 days to complete half the work.