Question:
2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6 women do the same work?
Solution:
Work of 2 men $=$ Work of 3 women
$\Rightarrow$ Work of 1 man $=\frac{3}{2}$ women
Three women can do a piece of work in 16 days.
As 4 men and 6 women $=\left(4 \times \frac{3}{2}\right)$ women $+6$ women $=6$ women $+6$ women $=12$ women
Also, 3 women can do the work in 16 days.
So, work done by 3 women in one day $=\frac{1}{16}$
$\therefore$ Work done by 1 woman in one day $=\frac{1}{48}$
$\Rightarrow$ Work done by 12 women in one day $=\frac{1}{4}$
Thus, 4 men and 6 women will complete the work in 4 days.