Two pipes $A$ and $B$ can fill a tank in $15$ hours and $20$ hours respectively,while a third pipe $C$ can empty the full tank in $25$ hours. All three pipes are opened in the beginning. After $10$ hours,pipe $C$ is closed. Find the total time (in hours) in which the tank will be full.

$A$ 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 inlet pipes can fill a cistern in $10$ $hours$ and $12$ $hours$ respectively,and an outlet pipe can empty $80$ $gallons$ of water per hour. All three pipes working together can fill the empty cistern in $20$ $hours$. What is the capacity (in $gallons$) of the tank?

Two pipes can fill a tank in $10$ $hours$ and $12$ $hours,$ while a third pipe can empty the full tank in $20$ $hours.$ If all three pipes operate simultaneously,in how much time will the tank be filled?

Two pipes $A$ and $B$ can fill a cistern in $20$ $minutes$ and $25$ $minutes$ respectively. Both are opened together,but after $5$ $minutes,$ $B$ is turned off. How much time (in $minutes$) longer will the cistern take to fill?

$A$ booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is $2400 m^3$. The emptying capacity of the tank is $10 m^3/min$ higher than its filling capacity and the pump needs $8$ minutes less to empty the tank than it needs to fill it. What is the filling capacity of the pump?