a) $${\text{5}}\frac{6}{{13}}{\text{ months}}$$
b) $${\text{6 months}}$$
c) $${\text{5}}\frac{7}{{13}}{\text{ months}}$$
d) $${\text{11}}\frac{1}{{13}}{\text{ months}}$$

Answer: d
Explanation: 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
$$\eqalign{ & {\text{10 men}} + \frac{{20}}{3} + 5 \cr & \Rightarrow \frac{{30 + 20 + 15}}{3} \cr} $$
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
$$\eqalign{ & = \frac{{6 \times 40}}{{\frac{{65}}{3}}} \cr & = 11\frac{1}{{13}}{\text{ months}} \cr} $$