Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days, ten adults left and four children joined them. How many days will they take to complete the remaining work?
Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days. Sixteen adults started working and after three days, ten adults left and four children joined them. How many days will they take to complete the remaining work?
Explanation
Work done by 12 children in 16 days = 1 (full work)
Work done by 1 child in 16 days = 1/12
Work done by 1 child in 1 day = 1/(12 × 16) = 1/192
Work done by 8 adults in 12 days = 1
Work done by 1 adult in 12 days = 1/8
Work done by 1 adult in 1 day = 1/(8 × 12) = 1/96
Work done by 16 adults in 3 days = 16 × 3 × (1/96) = 1/2
Remaining work = 1 - 1/2 = 1/2
Now, 6 adults and 4 children work together:
Work done by 6 adults in 1 day = 6 × 1/96 = 6/96 = 1/16
Work done by 4 children in 1 day = 4 × 1/192 = 4/192 = 1/48
Total work done per day = (1/16 + 1/48) = (3 + 1)/48 = 4/48 = 1/12
Days required = (1/2) ÷ (1/12) = 6 days