Two pipes $A$ and $B$ can fill a tank in $24$ and $32$ $min$,respectively. If both the pipes are opened together,after how much time pipe $B$ should be closed so that the tank is full in $9$ $min$ (in $min$)?

One fill pipe $A$ is $3$ times faster than second fill pipe $B$ and takes $32$ minutes less than the fill pipe $B$. When will the cistern be full if both the pipes are opened together?

If two pipes function simultaneously,the reservoir will be filled in $6$ $hours$. One pipe fills the reservoir $5$ $hours$ faster than the other. How many $hours$ does the faster pipe take to fill the reservoir?

Three taps $A, B$ and $C$ fill a tank in $20$ min,$15$ min and $12$ min,respectively. If all the taps are opened simultaneously,how long will they take to fill $40 \%$ of the tank (in $min$)?

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 $\text{minutes}$)

$A$ cistern has two pipes. One can fill it in $8 \, h$ and the other can empty it in $5 \, h$. In how many $hours$ will the cistern be emptied if both the pipes are opened together when $\frac{3}{4}$ of the cistern is already full of water?