A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in
Solution
Correct Answer: Option B
Let work done by (A + C) in 1 day be x
∵ A, B and C together can finish a work in 6 days
∴(A + B + C)'s 1 day's work = 1/6
Similarly, (A + B)'s 1 day's work = 1/8
(B + C)'s 1 day's work = 1/12
Work done by [(A + B) + (B + C) + (A + C)] in 1 day = 2 × work done by (A + B + C) in 1 day
∴(A + C)'s 1 day's work = 2 × work done by (A + B + C) in 1 day - Work done by [(A + B) + (B + C)]in 1 day
∴(A + C)'s 1 day's work = \(2 \times \frac{1}{6} - \left( {\frac{1}{8} + \frac{1}{{12}}} \right)\)
= 3/24
= 1/8
So, A and C together will do the work in 8 days.
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