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 = ?

Answer: Option B

According to the question,
$$\begin{array}{rl}& \text{2m}+\text{3w}=\text{4m}\\ & \text{3w}=\text{4m}-\text{2m }\\ & \text{3w}=\text{2m}\\ & \text{3m}+\text{3w}=\text{3m}+\text{2m}\\ & \text{3m}+\text{3w}=\text{5m}\end{array}$$
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

$$\begin{array}{rl}& \mathbf{Alternate}:\\ & \left(2\text{m}+\text{3w}\right)\times \text{20}=\text{4m}\times \text{20}\\ & \frac{\text{m}}{\text{w}}=\frac{3}{2}\\ & \text{Total work }\\ & \text{ = }\left(\text{2}\times \text{3}+\text{3}\times \text{2}\right)\times 20\\ & =240\text{units}\\ & \text{5 men efficiency}\\ & =5\times 3\\ & =15\\ & \text{Required number of days}\\ & =\frac{240}{15}\\ & =16\text{ days}\end{array}$$