Three taps $A, B$ and $C$ together can fill an empty cistern in $10$ $min.$ The tap $A$ alone can fill it in $30$ $min$ and the tap $B$ alone can fill it in $40$ $min.$ How long will the tap $C$ alone take to fill it? (in $minutes$)

$A$ tap having diameter $d$ can empty a tank in $40$ $min$. How long will another tap having diameter $2d$ take to empty the same tank (in $min$)?

Two pipes can fill a tank in $10$ $hours$ and $12$ $hours,$ while a third pipe can empty the full tank in $20$ $hours.$ If all three pipes operate simultaneously,in how much time will the tank be filled?

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?

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

$A$ water tank has three taps $A, B, C$. Tap $A$,when opened,can fill the water tank alone in $4$ hours. Tap $B$,when opened,can fill the water tank alone in $6$ hours,and tap $C$,when opened,can empty the water tank alone in $3$ hours. If taps $A, B,$ and $C$ are opened simultaneously,how long (in hours) will it take to fill the tank completely?