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?

Answer 1

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 $=(4\times \frac{3}{2})$ 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.