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Question
A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.
- How long will it take them to do the work together?
- In what time can each finish it working alone?
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Solution
A and B can do a piece of work in = 40 days
B and C can do a piece of work in = 30 days
C and A can do a piece of work in = 24 days
(A+B)’s 1-day work =`1/40`
(B+C)’s 1-day work =`1/30`
(C+A)’s 1-day work =`1/24`
(i) [(A+B)+(B+C)+(C+A)]’s 1 day work = `1/40+1/30+1/24`
`=(3+4+5)/120`
`=12/120=1/10`
i.e. (A+B+B+C+C+A)'s 1-day work =`1/10`
i.e. 2 (A+B+C)'s 1-day work =`1/10`
∴ (A+B+C)'s 1-day work =`1/10xx1/2`
`=1/20`
∴ (A+B+C) can do the work in = 20 days
(ii) A's 1-day work =`1/20-1/30`
`=(3-2)/60=1/60`
∴ A can do the work in 60 days
B's 1-day work =`1/20-1/24`
`=(6-5)/120=1/120`
∴ B can do the work in 120 days
now, C's 1-day work =`1/20-1/40`
`=(2-1)/40=1/40`
C can do the work in 40 days
Hence A can do the work in = 60 days
B can do the work in = 120 days
C can do the work in = 40 days
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