If 2 men or 6 women or 4 boys can finish a work in 99 days, how many days will one man, one woman and one boy together take to finish the same work ?

Answer: Option E

$$\begin{array}{rl}& \text{1 men’s 1 day’s work}\\ & =\frac{1}{99\times 2}\\ & =\frac{1}{198}\\ & \text{1 women’s 1 day’s work}\\ & =\frac{1}{99\times 6}.\\ & =\frac{1}{594}\\ & \text{1 boy’s 1 day’s work}\\ & =\frac{1}{99\times 4}\\ & =\frac{1}{396}\end{array}$$
(1 men + 1 women + boy)'s 1 day's work
$$\begin{array}{rl}& =\frac{1}{198}+\frac{1}{594}+\frac{1}{396}\\ & =\frac{11}{1188}\\ & =\frac{1}{108}\end{array}$$
Hence, 1 mens , 1 women and 1 boys together take 108 days to finish the work.