$A$ 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 $24$ $min.$ and $48$ $min.$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) $B$ should be closed so that the tank is full in $20$ $minutes$?

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?

Taps $A, B$ and $C$ are attached to a tank. The rates of water flow through them are $42 \ L/h$,$56 \ L/h$,and $48 \ L/h$ respectively. $A$ and $B$ are inlet taps,while $C$ is an outlet tap. If all the taps are opened simultaneously,the tank is filled in $16 \ h$. What is the capacity of the tank (in $L$)?

$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6$ $hrs$. $B$ and $C$ together fill the tank in $10$ $hrs$,and $C$ and $A$ together fill the tank in $7 \frac{1}{2}$ $hrs$. In how much time (in $hours$) will $A, B$ and $C$ fill the tank together?

$A$ cistern has a leak which would empty it in $8$ $hours$. $A$ tap is turned on which admits $6$ $litres$ a $minute$ into the cistern,and it is now emptied in $12$ $hours$. The cistern can hold (in $litres$):