Two pipes $A$ and $B$ can fill a tank in $37 \frac{1}{2}$ minutes and $45$ minutes respectively. If both pipes are opened together,after how much time (in minutes) should pipe $B$ be closed so that the tank is full in exactly $30$ minutes?

$18$ pumps can fill a reservoir of capacity $1440 \text{ kilo liter}$ in $5 \text{ hours}$. How many $\text{hours}$ are required to fill a reservoir of capacity $1920 \text{ kilo liter}$ by $8$ pumps?

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?

$A$ swimming pool is fitted with three pipes. The first two pipes working simultaneously fill the pool in the same time as the third pipe alone. The second pipe alone fills the pool $5$ hours faster than the first pipe and $4$ hours slower than the third pipe. In what time (in hours) will the second and third pipes together fill the pool?

Pipe $A$ can fill an empty tank in $6$ $hours$ and pipe $B$ in $8$ $hours$. If both the pipes are opened and after $2$ $hours$ pipe $A$ is closed,how much time will pipe $B$ take to fill the remaining tank?

Two taps $A$ and $B$ can fill a tank in $20 \text{ min}$ and $30 \text{ min}$,respectively. An outlet pipe $C$ can empty the full tank in $15 \text{ min}$. If $A, B$,and $C$ are opened alternatively,each for $1 \text{ min}$,how long (in $\text{min}$) will the tank take to be filled?