A small hole in the bottom of a cistern can empty the full container in 360 minutes. An inlet pipe fills water at the rate of 4 liters a minute. When the container is full, the inlet is opened and due to the leak, the cistern is empty in 24 hours. How many liters does the cistern hold?

The inlet pipe fills water at 4 liters per minute, while the leak empties the full cistern in 360 minutes, meaning the leak's rate is Capacity/360. When both are open, the net emptying rate is 1/24 per minute, so we set up the equation 1/24 = 1/360 - 4/Capacity. Multiplying by the capacity gives Capacity/24 = Capacity/360 - 4, which simplifies to 14(Capacity)/360 = 4. Solving this yields a capacity of 1440/0.75, so the cistern holds 1920 liters.

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