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 ?

Solution(By Examveda Team)

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