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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?

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#### 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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