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?

Two pipes $A$ and $B$ can fill a cistern in $4$ $minutes$ and $6$ $minutes,$ respectively. If these pipes are turned on alternately for $1$ $minute$ each,then how long will it take for the cistern to fill?

Pipes $P$ and $Q$ can fill a tank in $5$ and $6 \, h$, respectively, and pipe $C$ can empty it in $3 \, h$. If all the three are opened at $7 \, am$, at what time will two-fifths of the tank be filled?

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?

$A$ cistern has $3$ pipes $A, B$ and $C$. Pipes $A$ and $B$ can fill it in $3$ and $4$ hours respectively,and pipe $C$ can empty it in $1$ hour. If the pipes are opened at $3 \text{ pm}$,$4 \text{ pm}$,and $5 \text{ pm}$ respectively on the same day,at what time will the cistern be empty?

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?