If 16 men or 20 women can do a piece of work in 25 days. In what time will 28 men and 15 women do it ?

Solution(By Examveda Team)

If number of days at work is same
$$\eqalign{ & {\text{So, we can equate directly}} \cr & {\text{16 men}} = {\text{20 women}} \cr & {\text{4 men}} = {\text{5 women}} \cr & {\text{5 women}} = {\text{4 men}} \cr & {\text{1 women}} = \frac{4}{5}{\text{men}} \cr & {\text{15 women}} = \frac{4}{5} \times {\text{15}} \cr & {\text{15 women}} = {\text{12 men}} \cr} $$
⇒ 16 men complete a work in 25 days
1 men complete a work in 400 days
$$\eqalign{ & 28{\text{ men}} + {\text{15 women}} = ? \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow \cr & 28{\text{ men}} + {\text{12 men}} = {\text{40 men}} \cr & {\text{work in }} = \frac{{25 \times 16}}{{40}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{10 days}} \cr & \cr & {\bf{Alternate:}} \cr & {\text{16 m or 20 w}} \to {\text{25 days}} \cr & {\text{28 m and 15 w}} \to {\text{?}} \cr & \frac{{16 \times 20 \times 25}}{{\left( {16 \times 15} \right) + \left( {20 \times 28} \right)}} \cr & = 10{\text{ days}} \cr} $$