$A$ 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 $litres$):

Two pipes $A$ and $B$ can fill a water tank in $10$ and $12$ $min,$ respectively,and a third pipe $C$ can empty it at the rate of $6$ $gallons$ per $min.$ If $A, B,$ and $C$ are opened together,they fill the tank in $20$ $min.$ What is the capacity (in $gallons$) of the tank?

Two pipes $A$ and $B$ can fill a cistern in $15$ and $20$ $min$,respectively. Both the pipes are opened together,but after $2$ $min$,pipe $A$ is turned off. What is the total time (in $minutes$) required to fill the tank?

If two pipes function simultaneously,the reservoir will be filled in $6$ $hours$. One pipe fills the reservoir $5$ $hours$ faster than the other. How many hours does the faster pipe take to fill the reservoir?

An outlet pipe can empty a cistern in $3$ $h$. In what time (in $h$) will the pipe empty two-third part of the cistern?

Having the same capacity,$9$ taps fill up a water tank in $20$ minutes. How many taps of the same capacity are required to fill up the same water tank in $15$ minutes?