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Question
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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