As per the question,

In 5 minutes both the pipes together can fill,

$5\times \left(\frac{1}{20}+\frac{1}{25}\right)=\frac{5}{20}+\frac{5}{25}=\frac{1}{4}+\frac{1}{5}=\frac{9}{20}$^th pat of tank

Part filled by first pipe,

$1-\frac{9}{20}=\frac{11}{20}$^th part

So, 

$\frac{18\times 6}{18-6}=\frac{108}{12}=9 \mathrm{minutes}$

Hence in 9 Minutes the waste pipe can empty the full cistern.

Hence option A is correct.