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Question
A can do a piece of work in 24 days, A and B can do it in 16 days and A, B, and C in `10 2/3` days. In how many days can A and C do it working together?
Solution
A can do a piece of work in = 24 days
(A+B) can do a piece of work in = 16 days
(A+B+C) can do a piece of work in
`=10 2/3`days = `32/3` days
∴ A's 1-day work =`1/24`
(A+B)'s 1 day work =`1/16`
(A+B+C)'s 1 day work =`3/32`
C's 1 day work =`3/32-1/16`
`=(3-2)/32=1/32`
(A+C)'s 1-day work =`1/24+1/32`
`=(4+3)/96=7/96`
∴ (A+C) can do the work in =`96/7` days
`=13 5/7` days
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