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Question
A can do a piece of work in 12 hours, B and C can do it 3 hours whereas A and C can do it in 6 hours. How long will B alone take to do the same work?
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Solution
Time taken by A to complete the work = 12 hours.
∴ A’s 1 hour work = `1/12` ...(1)
(B + C) complete the work in 3 hours.
∴ (B + C)’s 1 hour work = `1/3` ...(2)
Add (1) and (2)
∴ (A + B + C)’s 1 hour work = `1/12 + 1/3`
= `(1 + 4)/12`
= `5/12`
Now (A + C) complete the work in 6 hours.
∴(A + C)’s 1 hour work = `1/6`
∴ B’s 1 hour work = (A + B + C)’s 1 hour work – (A + C)’s 1 hour work
= `5/12 - 1/6`
= `(5 - 2)/12`
= `3/12`
= `1/4`
∴ B alone take 4 days to complete the work.
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