18 men can complete a piece of work in 63 days. 9 women take 189 days to complete the same piece of work. How many days will 4 men, 9 women and 12 children together take to complete the piece of work if 7 children alone can complete the piece of work in 486 days ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{63 \times 18}} \cr & = \frac{1}{{1134}} \cr & {\text{1 women's 1 day's work}} \cr & = \frac{1}{{189 \times 9}} \cr & = \frac{1}{{1701}} \cr & {\text{1 children's 1 day's work}} \cr & = \frac{1}{{486 \times 7}} \cr & = \frac{1}{{3402}} \cr} $$
(4 men + 9 women + 12 children)'s 1 day's work
$$\eqalign{ & = \frac{4}{{1134}} + \frac{9}{{1701}} + \frac{{12}}{{3402}} \cr & = \frac{{42}}{{3402}} \cr & = \frac{1}{{81}} \cr} $$
Hence, 4 mens , 9 women and 12 children together will complete the work in 81 days.