To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :

Answer: Option C

Given (A+B)'s one day's work = $$\frac{1}{8}$$
(B + C)'s one day's work = $$\frac{1}{12}$$
(A + B + C) 's 1 day's work = $$\frac{1}{6}$$

Work done by A, alone= (A + B + C) 's 1 day's work - (B + C)'s one day's work
$$=\frac{1}{6}-\frac{1}{12}=\frac{2-1}{12}=\frac{1}{12}$$
Work done by C, alone = (A + B + C) 's 1 day's work - (A + B)'s one day’s work
$$=\frac{1}{6}-\frac{1}{8}=\frac{4-3}{24}=\frac{1}{24}$$
⇒ (A + C)’s one day’s work
$$\begin{array}{rl}& =\frac{1}{12}+\frac{1}{24}\\ & =\frac{2+1}{24}\\ & =\frac{3}{24}=\frac{1}{8}\end{array}$$
⇒ (A + C) will take 8 days to complete the work together