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,

 $$\begin{gathered} \frac{10\times 15\times x}{(10\times 15)+(10\times x)+(15\times x)}=12 \\ \frac{150x}{150+10x+15x}=12 \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} 150x=12 \left(150+10x+15x\right) \\ 150x=\left(150\times 12\right)+\left(25x\times 12\right) \\ 150x=1800+300x \\ 1800=300x-150x \\ 1800=150x \\ x=\frac{1800}{150}=-12 \end{gathered}$$

Here negative sign implies that the pipe is a waste pipe and it emties the water in the tank in 12 hours.   

Hence option A is correct.