$A$ tap takes $36$ hours extra to fill a tank due to a leakage equivalent to half of its inflow. In how many hours can the inlet pipe alone fill the tank?

If two pipes function together,the tank will be filled in $12$ $h$. One pipe fills the tank $10$ $h$ faster than the other. How many $h$ does the faster pipe take to fill up the tank?

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?

$A$ tap can fill an empty tank in $12$ $hours$ and another tap can empty the half-filled tank in $10$ $hours$. If both the taps are opened together,then how much time (in $hours$) will it take to fill an empty tank half-filled?

$A$ tank can be filled by pipe $A$ in $2$ $hours$ and pipe $B$ in $6$ $hours.$ At $10 \, am$ pipe $A$ was opened. At what time will the tank be filled if pipe $B$ is opened at $11 \, am$?

Two taps can fill a tank in $20$ $min$ and $30$ $min$ respectively. When the tank was empty,both the taps were opened,and after some time,the first tap was closed. It took $18$ $min$ in total to fill the tank. After how much time (in $minutes$) from the beginning was the first tap closed?