A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 8 days. A, B and C together can complete it in

Let the rate of work done by A, B and C be $$ \frac{1}{A} , \frac{1}{B} and \frac{1}{C}$$
$$(\frac{1}{A} + \frac{1}{B}) = \frac{1}{8}$$ ------------------- 1
$$(\frac{1}{B} + \frac{1}{C}) = \frac{1}{12}$$ ------------------- 2
$$(\frac{1}{A} + \frac{1}{C}) = \frac{1}{8}$$ ------------------- 3
Adding 1 , 2 and 3
$$2 \times (\frac{1}{A} + \frac{1}{B} + \frac{1}{C}) = \frac{1}{8} + \frac{1}{12} + \frac{1}{8} = = \frac{1}{4} + \frac{1}{12} = \frac{1}{3} $$
$$(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}) = \frac{1}{6}$$
It takes 6 days for all to complete the work.
Hence Option C is the correct answer.