2 men or 3 women can do a piece of work in 16 days.
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.

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