Let us suppose the fester pipe fills the tank in x hours

and then the slower pipe fills the tank in x+10 hours

When both the pipes are opened together, the reserviour will be filled in 12 hours

 $$\begin{gathered} \frac{\mathrm{x}\left(\mathrm{x}+10\right)}{x+(x+10)}=12 \\ \frac{x^2+10x}{x+x+10}=12 \end{gathered}$$

Upon cross multiplication,

$$\begin{gathered} {\mathrm{x}}^2+10\mathrm{x}=12\left[\mathrm{x}+\mathrm{x}+10\right] \\ {\mathrm{x}}^2+10\mathrm{x}=12\mathrm{x}+12\mathrm{x}+120 \\ {\mathrm{x}}^2-14\mathrm{x}-120=0 \\ \therefore x=20 or -6 \end{gathered}$$

Because x cannot take negative value, the faster pipe will fill the reservoir in 20 hours.

Hence option A is correct.