$A$ cistern has a leak which would empty it in $8$ $hours$. $A$ tap is turned on which admits $6$ $litres$ a $minute$ into the cistern,and it is now emptied in $12$ $hours$. The cistern can hold (in $litres$):

$A$ swimming pool is fitted with three pipes. The first two pipes working simultaneously fill the pool in the same time as the third pipe alone. The second pipe alone fills the pool $5$ hours faster than the first pipe and $4$ hours slower than the third pipe. In what time (in hours) will the second and third pipes together fill the pool?

$A$ 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?

Three pipes $A, B$ and $C$ can fill a cistern in $10$ $hours$,$12$ $hours$ and $15$ $hours$ respectively. First $A$ was opened. After $1$ $hour$,$B$ was opened and after $2$ $hours$ from the start of $A$,$C$ was also opened. Find the time in which the cistern is just full.

$A$ 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?

$A$ cistern has a leak which would empty it in $8$ $hours$. $A$ tap is turned on which admits $6$ $litres$ a minute into the cistern,and it is now emptied in $12$ $hours$. How many $litres$ does the cistern hold?