Two pipes $A$ and $B$ can fill a tank in $24$ $min.$ and $48$ $min.$ respectively. If both the pipes are opened simultaneously,after how much time (in $minutes$) $B$ should be closed so that the tank is full in $20$ $minutes$?

$10$ buckets of water fill a tank when the capacity of each bucket is $12$ litres. How many buckets will be needed to fill the same tank,if the capacity of each bucket is $8$ litres?

$A$ cistern is normally filled in $8$ $hours$,but it takes $2$ $hours$ longer to fill because of a leak at its bottom. If the cistern is full,the leak will empty it in (in $hours$):

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

$A$ pipe can fill a cistern in $4$ $min$ and another pipe can fill it in $5$ $min,$ but a third pipe can empty it in $2$ $min.$ The first two pipes are kept open for $2$ $min$ in the beginning and then the third pipe is also opened. Time (in $min$) taken to empty the cistern is?

Inlet $A$ is four times faster than inlet $B$ to fill a tank. If inlet $A$ alone can fill it in $15$ minutes,how long will it take if both the pipes are opened together? (in minutes)