According to the above given formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

According to the question x+y+z=10

So,

 $$\begin{gathered} 5=\frac{20\times 10\times \mathrm{z}}{(20\times 10)+(10\times \mathrm{z})+(\mathrm{z}\times 20)} \\ 5=\frac{200\mathrm{z}}{200+10\mathrm{z}+20\mathrm{z}} \\ 5=\frac{200\mathrm{z}}{200+30\mathrm{z}} \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} 5\left(200+30\mathrm{z}\right)=200\mathrm{z} \\ 1000+150\mathrm{z}=200\mathrm{z} \\ 1000=200\mathrm{z}-150\mathrm{z} \\ 1000=50\mathrm{z} \\ \mathrm{z}=\frac{1000}{50} \\ \mathrm{z}=20 \mathrm{minutes} \end{gathered}$$

Therefore, the tank will be emptied in 20 minutes.

Hence option B is correct