$A$ pipe can fill a tank with water in $5$ $hours$ and another pipe can empty the same tank in $4$ $hours$. If the tank is completely filled and both the taps are opened together,in how much time $(hours)$ will the tank be empty?

$A$ 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 filled in $20$ $minutes$. How long will the waste pipe take to empty a full cistern?

Two pipes $A$ and $B$ can fill a cistern in $24$ $minutes$ and $30$ $minutes$,respectively. There is also an outlet $C$. If all the three pipes are opened together,the cistern is full in $20$ $minutes$. How much time (in $minutes$) will be taken by outlet $C$ to empty the full cistern?

In what time would a cistern be filled by three pipes whose diameters are $1 \text{ cm}$,$1 \frac{1}{3} \text{ cm}$,and $2 \text{ cm}$,running together,when the largest alone will fill it in $61 \text{ minutes}$,the amount of water flowing in by each pipe being proportional to the square of its diameter? (in $\text{minutes}$)

Two pipes $A$ and $B$ can fill a tank in $15$ minutes and $20$ minutes respectively. Both the pipes are opened together but after $4$ minutes,pipe $A$ is turned off. What is the total time required to fill the tank?

$A$ water tank is $\frac{2}{3}$ full. Pipe $A$ can fill the tank in $10$ $minutes$ and pipe $B$ can empty it in $6$ $minutes$. If both the pipes are open,how long will it take to empty the tank completely?