According to the question,

In 1 day,

A can complete $\frac{1}{12}$^th of the work 

B can complete $\frac{1}{24}$^th of the work

C can complete $=\frac{1}{36}$^th of the work

Then, (A+B+C) together can complete 

$$\begin{gathered} =\frac{1}{12}+\frac{1}{24}+\frac{1}{36} \\ =\frac{6+3+2}{72}=\frac{11}{72} \end{gathered}$$

∴ (A+B+C) together will complete the work in $\frac{72}{11} or 6\frac{6}{11} days$

Hence option C is the correct.