Time taken to complete the work by

C=x days

A=3x days

According to the question,

$$\begin{gathered} =\frac{1}{3x}+\frac{1}{{\displaystyle \frac{3x}{2}}}+\frac{1}{x}=1 \\ =\frac{1}{3x}+\frac{2}{3x}+\frac{1}{x}=1 \\ =\frac{1+2+3}{3x}=1 \\ \Rightarrow \frac{6}{3x}=1 \end{gathered}$$

$$\begin{gathered} \Rightarrow \frac{2}{x}=1 \\ \therefore x=2 \end{gathered}$$

Time taken to by Ais 3x

So, 3×2=6 days

Hence option C is the correct.