Two pipes $A$ and $B$ can fill a tank in $36$ $hours$ and $45$ $hours$ respectively. If both the pipes are opened simultaneously,how much time (in $hours$) will be taken to fill the tank?

$A$ pipe can fill a tank with thrice the speed of another pipe. If both the pipes together take $36$ $min$ to fill an empty tank completely,then how much time will it take for the slower pipe to fill the tank alone?

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?

$10$ 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?

$A$ water tank has two pipes. The empty tank is filled in $12$ $min$ by the $1$st pipe and the full tank is emptied by the $2$nd pipe in $20$ $min$. What is the time required to fill the $1/2$ full tank when both pipes are in action (in $min$)?

$A$ booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is $2400 m^3$. The emptying capacity of the tank is $10 m^3/min$ higher than its filling capacity and the pump needs $8$ minutes less to empty the tank than it needs to fill it. What is the filling capacity of the pump?