If 40 men or 60 women or 80 children can do a piece of work in 6 months, then 10 men, 10 women and 10 children together do the work in ?

Answer: Option D

40 men = 60 women = 80 children
2 men = 3 women = 4 children
2 men = 3 women
1 women = $$\frac{2}{3}$$ men → 10 women
$$\to \frac{2}{3}\times 10=\frac{20}{3}\text{ men}$$
Similarly
2 men = 4 children
1 children = $$\frac{1}{2}$$ men → 10 children
$$=\frac{10}{2}=\text{5 men}$$
10 men = 10 women = 10 children
$$\begin{array}{rl}& \text{10 men}+\frac{20}{3}+5\\ & \Rightarrow \frac{30+20+15}{3}\end{array}$$
10 men + 10 women + 10 children = $$\frac{65}{3}$$ men
40 men can do a piece of work in 6 months
1 men can do a piece of work in 6 × 40
$$\frac{65}{3}$$ men can do a piece of work in
$$\begin{array}{rl}& =\frac{6\times 40}{\frac{65}{3}}\\ & =11\frac{1}{13}\text{ months}\end{array}$$

Alternate :
40 men = 60 women = 80 children
2 men = 3 women = 4 children
men : women : children = 6 : 4 : 3 (efficiency)
∴ Total work
$$\begin{array}{rl}& =40\times 6\times 6\\ & =1440\text{units}\end{array}$$
Total time taken by (40 men + 60 women + 80 children)
$$\begin{array}{rl}& =\frac{\text{Total work}}{\text{Efficiency}}\\ & =\frac{1440}{130}\\ & =11\frac{1}{13}\text{months}\end{array}$$