One tap can fill a cistern in $2$ $hours$ and another can empty the cistern in $3$ $hours.$ How long will they take to fill the cistern if both the taps are opened?

$A, B$ 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 two taps which fill it in $12$ $minutes$ and $15$ $minutes,$ respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in $20$ $minutes.$ How long will the waste pipe take to empty a full cistern?

$A$ tank can be filled by one tap in $20$ $minutes$ and by another in $25$ $minutes$. Both the taps are kept open for $5$ $minutes$ and then the second is turned off. In how many $minutes$ more will the tank be completely filled?

$A, B, C$ are pipes attached to a cistern. $A$ and $B$ can fill it in $20$ and $30$ minutes respectively,while $C$ can empty it in $15$ minutes. If $A, B, C$ are kept open successively for $1$ minute each,how soon will the cistern be filled? (in minutes)

Two pipes $A$ and $B$ can fill a cistern in $18$ $minutes$ and $9$ $minutes$ respectively,while a third pipe $C$ can empty the full tank in $5$ $minutes$. $A$ and $B$ are kept open for $4$ $minutes$ in the beginning and then $C$ is also opened. In what time (in $minutes$) is the cistern emptied?