A cistern has a leak which can empty the full cistern in 12 hours. A tap that lets in 20 litres a minute is turned on, and the full cistern is now emptied in 20 hours. How many litres does the cistern hold?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 36000
With the tap on, the cistern still empties, only more slowly. The tap's filling rate is the leak's rate minus the net emptying rate. Comparing this fraction of the cistern with 20 litres a minute gives the capacity.
Leak alone empties \(\frac{1}{12}\) of the cistern per hour; with the tap on, the net emptying is \(\frac{1}{20}\) per hour
Tap fills \(\displaystyle \frac{1}{12}-\frac{1}{20}=\frac{5-3}{60}=\frac{1}{30}\) of the cistern per hour
Tap lets in \(20\times60=1200\) litres per hour
Capacity \(=1200\times30=36000\) litres