According to the question,

In 1 day,

(A+B) can complete $\frac{1 }{18}$^th of the work

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

B alone can complete,

              $$\begin{gathered} =\frac{1}{18}-\frac{1}{36} \\ =\frac{2-1}{36}=\frac{1}{36} \end{gathered}$$

 ∴ B alone can finish the work in 36 days.

 Hence option C is the correct.