9 children can complete a piece of work in 360 days. 18

Solution

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