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Question

A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?


Solution

A and B can do a work in = 8 days
B and C can do a work in = 12 days
A and C can do a work in = 16 days
(A+B)'s 1 day work =18
(B+C)'s 1 day work =112
(A+C)'s 1 day work =116
[(A+B)+(B+C)+(A+C)]'s 1 day work
=18+112+116
i.e. [A+B+B+C+A+C]'s 1 day work
=18+112+116
=6+4+348=1348
i.e. 2(A+B+C)'s 1 day work =1348
i.e. (A + B + C)'s 1 day work =1348×12=1396
(A + B + C) can do the work in =9613 days
=7513 days.

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