Pipe $\mathrm{A}$ can fill an empty tank in $5$ hours while pipe $\mathrm{B}$ can empty the full tank in $6$ hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up completely?

Three taps $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ can fill an overhead tank in $6$ hours, $8$ hours and $12$ hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened together?

A cistern has two inlets $\mathrm{A}$ and $\mathrm{B}$ which can fill it in $12$ minutes and $15$ minutes respectively. An outlet $\mathrm{C}$ can empty the full cistern in $10$ minutes. If all the three pipes are opened together in the empty tank, how much time will they take to fill the tank completely?

A pipe can fill a cistern in $9$ hours. Due to a leak in its bottom, the cistern fills up in $10$ hours. If the cistern is full, in how much time will it be emptied by the leak?

Pipe $\mathrm{A}$ can fill a cistern in $6$ hours and pipe $\mathrm{B}$ can fill it in $8$ hours. Both the pipes are opened and after two hours, pipe $\mathrm{A}$ is closed. How much time will $\mathrm{B}$ take to fill the remaining part of the tank?