Six women alone can complete a piece of work in 10 days whereas 10 children alone take 15 days to complete the same piece of work. How many days will 6 women and 10 children together take to complete the piece of work ?

6 women take 10 days to complete a piece of work.
So, the amount of work done by 6 women in 1 day is $$\frac{1}{10}$$

10 children take 15 days to complete a piece of work.
So, the amount of work done by 10 children in 1 day is $$\frac{1}{15}$$

So, the amount of work done by 6 women and 10 children in 1 day is $$\frac{1}{10}+\frac{1}{15} = \frac{1}{6}$$

Hence, the number of days taken by 6 women and 10 children to complete the piece of work is 6 days.