$A$ tap can fill a tank in $25$ $minutes$ and another can empty it in $50$ $minutes$. Find out whether the tank will be filled up or emptied and in how many $minutes$?

If three taps are opened together,a tank is filled in $12$ $hrs$. One of the taps can fill it in $10$ $hrs$ and another in $15$ $hrs$. How many $hours$ does the third tap take alone to empty it completely?

Pipe $A$ can fill a tank in $5$ $hours$,pipe $B$ in $10$ $hours$,and pipe $C$ in $30$ $hours$. If all the pipes are opened,in how many $hours$ will the tank be filled?

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?

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 $\text{minutes}$)

$A$ pipe can fill a tank in $10 \, h$, while another pipe can empty it in $6 \, h$. Find the time (in $hours$) taken to empty the tank when both the pipes are opened simultaneously.