Let the faster pipe fill the tank in x hours.

then the slower pipe fills in (x+5) hours

According tot he question, both the pipes together can fill the tank in 6 hours.

$$\begin{gathered} \Rightarrow \frac{\mathrm{x}\left(\mathrm{x}+5\right)}{\mathrm{x}+\mathrm{x}+5}=6 \mathrm{hours} \\ \Rightarrow {\mathrm{x}}^2+5\mathrm{x}=12\mathrm{x}+30 \\ \Rightarrow {\mathrm{x}}^2-7\mathrm{x}-30=0 \end{gathered}$$

X can take value either 10 or -3

As the question is about the pipe that fills faster, we will neglect negative value

Therefore, the faster tap fills the tank in 10 hours.

Hence option D is correct.