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A and B complete a piece of work in 24 days. B and C do the same work in 36 days; and A, B, and C together finish it in 18 days. In how many days will:**(i) **A alone,**(ii) **C alone,**(iii)** A and C together, complete the work?

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#### Solution

A and B complete a piece of work in = 24 days

B and C complete a piece of work in = 36 days

(A+B+C) complete a piece of work in = 18 days

(A+B)’s 1-day work = `1/24`

(B+C)’s 1-day work = `1/36`

(A+B+C)’s 1-day work = `1/18`

**(i) **A's 1-day work =`1/18-1/36`

`=(2-1)/36=1/36`

∴ A will complete the work in = 36 days

**(ii)** C's 1-day work =`1/18-1/24`

`=(4-3)/72=1/72`

∴ C will complete the work in = 72 days

**(iii)** (A+C)'s 1-day work =`1/36+1/72`

`=(2+1)/72=3/72`

`=1/24`

∴ (A+C) will complete the work in = 24 days

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