According to the 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.

So,

 $$\begin{gathered} \frac{3\times 4\times 5}{(4\times 5)+(3\times 5)-(3\times 4)} \\ =\frac{60}{20+15-12}=\frac{60}{23} \mathrm{or} 2\frac{14}{23}\mathrm{hours} \end{gathered}$$

Hence, the tank will be filled in $2\frac{14}{23}$ hours when all the pipes are opened simultaneously.

Hence option B is correct.