2 men and 3 women together or 4 men can complete a piece of work in 20 days. 3 men and 3 women will complete the same work in = ?

Solution(By Examveda Team)

According to the question,
$$\eqalign{ & {\text{2m}} + {\text{3w}} = {\text{4m}} \cr & {\text{3w}} = {\text{4m}} - {\text{2m }} \cr & {\text{3w}} = {\text{2m}} \cr & {\text{3m}} + {\text{3w}} = {\text{3m}} + {\text{2m}} \cr & {\text{3m}} + {\text{3w}} = {\text{5m}} \cr} $$
4 men can do work in 20 days
1 men can do work in 20 × 4 days
5 men can do work in $$\frac{{{\text{20}} \times {\text{4}}}}{5}$$  = 16 days

$$\eqalign{ & {\bf{Alternate:}} \cr & \left( {2{\text{m}} + {\text{3w}}} \right) \times {\text{20}} = {\text{4m}} \times {\text{20}} \cr & \frac{{\text{m}}}{{\text{w}}} = \frac{3}{2} \cr & {\text{Total work }} \cr & {\text{ = }}\left( {{\text{2}} \times {\text{3}} + {\text{3}} \times {\text{2}}} \right) \times 20 \cr & = 240\,{\text{units}} \cr & {\text{5 men efficiency}} \cr & = 5 \times 3 \cr & = 15 \cr & {\text{Required number of days}} \cr & = \frac{{240}}{{15}} \cr & = 16{\text{ days}} \cr} $$