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Question
A can do a piece of work in 10 days; B in 18 days; and A, B, and C together in 4 days. In what time would C alone do it?
Solution
A can do a piece of work in = 10 days
B can do a piece of work in = 18 days
(A+B+C) can do a piece of work in = 4 days
∴ A's 1-day work =`1/10`
B's 1-day work = `1/18`
(A+B)'s 1-day work =`1/10+1/18=(9+5)/90`
`=14/90=7/45`
(A+B+C)'s 1-day work =`1/4`
∴ C's 1-day work =`1/4-7/45`
`=(45-28)/180=17/180`
∴ C can do the piece of work in = `180/17` days
`=10 10/17` days
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