9 children can complete a piece of work in 360 days. 18 men can complete the same piece of work in 72 days and 12 women can complete the piece of work in 162 days. In how many days can 4 men, 12 women and 10 children together completer the piece of work?

9 children can complete a work in 360 days. 1 child can complete a work in 9 × 360 days = 3,240 days ∴10 children can complete a work in3240/10 days = 324 days 18 men can complete a work in 72 days. 1 men can complete a work in 18 × 72 days = 1,296 days ∴4 men can complete a work in 1296/4 = 324 days 12 women can complete a work in 162 days. Now, 4 men + 12 women + 10 children’s work =1/324+ 1/162+1/324 = (1+2+1)/324 = 4/324= 1/81work Therefore, 4 men, 12 women and 10 children can complete a work in 81 days. Alternate Method: lets make time of all 3 equal , we can see 18 is common in 360, 72 and 162 So 180C or 72M or 108 W can do this job in = 18 days Hence 10c & 4M & 12 W can do this job in = 18/{10/180 + 4/72 + 12/108} = 18/ {1/18 + 1/18 + 1/9} = 18/ (4/18) = 81 days