Let us consider the third pipe to be a filling pipe which fills the tank in x hours

then, 

According to the If three pipes A, B and C can fill the tank separately in x hours, y hours and z hours respectively then, the time taken by all the three pipes together to fill the tank is  $\frac{\mathrm{xyz}}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$ hours.

So,

 $$\begin{gathered} \frac{19\times 20\times x}{(19\times 20)+(19\times x)+(20\times x)}=15 \\ \frac{380x}{380+19x+20x}=15 \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} 380x=15 \left(380+19x+20x\right) \\ 380x=\left(380\times 15\right)+\left(29x\times 15\right) \\ 380x=5700+435x \\ 5700=435x-380x \\ 5700=55x \\ x=-\frac{5700}{55}=-103 \end{gathered}$$

Here negative sign implies that the pipe is a waste pipe and it emties the water in the tank in 103 hours.

Hence option A is correct.