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?

$A$ 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 $12$ $hours$. How many $litres$ does the cistern hold?

$A$ pump can fill a tank with water in $2$ $hours$. Because of a leak,it took $2 \frac{1}{3}$ $hours$ to fill the tank. The leak can drain all the water of the tank in (in $hours$)?

Three pipes $A, B$ and $C$ can fill a tank from empty to full in $30$ minutes,$20$ minutes and $10$ minutes respectively. When the tank is empty,all the three pipes are opened. $A, B$ and $C$ discharge chemical solutions $P, Q$ and $R$ respectively. What is the proportion of solution $R$ in the liquid in the tank after $3$ minutes?

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.

Three taps $A, B$ and $C$ can fill a tank in $12, 15$ and $20$ hours respectively. If $A$ is kept open all the time,and $B$ and $C$ are opened for one hour each alternately,how long will it take to fill the tank?