If P and Q together finish a piece os work in x days, and P alone can comple the same work in y days, then the time taken by B to complete the same work will be $\frac{\mathrm{xy}}{y-x}$days.

So, 

$\frac{18\times 12}{18-12}=\frac{216}{6}=36 days$

 Hence option A is correct