A leak in the bottom of a tank can empty the full tank in $8$ hour. An inlet pipe fills water at the rate of $6$ liters a minutes. When the tank is full the inlet is opened and due to leak the tank is empty in $12$ hours. How many liters does the cistern hold ?

Using the net work rate formula, the inlet pipe must overcome the leak that empties the tank at a rate of one eighth per hour. Since the full tank empties in twelve hours when the inlet is open, the net emptying rate is one twelfth per hour. The inlet pipe's filling rate is one eighth minus one twelfth, which equals one twenty-fourth per hour, meaning the inlet takes twenty-four hours to fill the tank alone. Because the inlet adds six liters per minute, multiplying six by the total minutes in twenty-four hours, which is one thousand four hundred forty, gives a total capacity of eight thousand six hundred forty liters.

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