If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work ?

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{3m}} \times {\text{16}} = {\text{6w}} \times {\text{16}} \cr} $$
$$\frac{{\text{m}}}{{\text{w}}} = $$ $$\frac{{2 \to {\text{Efficiency of men}}}}{{1 \to {\text{Efficiency of women}}}}$$
$$\eqalign{ & {\text{Total work}} = 3 \times 2 \times 16 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 96{\text{ units}} \cr} $$
$${\text{One day work of}}$$    $$\left( {{\text{12m}} + {\text{8w}}} \right)$$
$$\eqalign{ & = 12 \times 2 + 8 \times 1 \cr & = 32{\text{ units}} \cr} $$
$${\text{Total time taken by}}$$    $$\left( {{\text{12m}} + {\text{8w}}} \right)$$
$$\eqalign{ & = \frac{{96}}{{32}} \cr & = 3{\text{ days}} \cr} $$