$A$ pipe can fill a tank with water in $3 \, h$. Due to a leak at the bottom,it takes $3 \frac{1}{2} \, h$ to fill it. In what time (in $hours$) will the leak empty the fully filled tank?

$A$ cistern can be filled by a tap in $4$ $hours$,while it can be emptied by another tap in $9$ $hours$. If both the taps are opened simultaneously,then after how much time (in $hours$) will the cistern get filled?

Two pipes $A$ and $B$ can fill a tank in $30$ $minutes$ and $45$ $minutes$ respectively. Pipe $C$ can empty the full tank in $36$ $minutes$. Initially,pipes $A$ and $B$ are opened. After $12$ $minutes$,pipe $C$ is also opened. What is the total time (in $minutes$) required to fill the tank?

Two pipes $A$ and $B$ can fill a cistern in $4$ $minutes$ and $6$ $minutes,$ respectively. If these pipes are turned on alternately for $1$ $minute$ each,then how long will it take for the cistern to fill?

Three pipes $A, B$ and $C$ can fill a tank in $6$ hours. After working together for $2$ hours,$C$ is closed and $A$ and $B$ fill the remaining part in $7$ hours. The number of hours taken by $C$ alone to fill the tank is:

$A$ tap can fill a tank in $6$ $h$. After half the tank is filled,three more similar taps are opened. What is the total time taken to fill the tank completely?