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1. 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 :

A. 4 days

B. 6 days

C. 8 days

D. 12 days

Solution:

\begin{aligned} (A + B + C)'s 1 day's work = \frac{1}{6} \\ (A + B)'s 1 day's work = \frac{1}{8} \\ (B + C)'s 1 day's work = \frac{1}{12} \\ ∴ (A + C)'s 1 day's work \\ = (2 \times \frac{1}{6}) - (\frac{1}{8} + \frac{1}{12}) \\ = \frac{1}{3} - \frac{5}{24} \\ = \frac{3}{24} \\ = \frac{1}{8} \end{aligned}

So, A and C together will do the work in 8 days

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