An overhead cistern of capacity 3,600 litres stands empty. Two inlets, delivering 90 litres and 60 litres a minute, are opened at 6:00 a.m. At 6:12 a.m. a drain that removes 60 litres a minute is opened by mistake and is left running. At what time is the cistern full?

The inlets together deliver 150 litres a minute, so by 6:12 a.m. they have put in 1,800 litres and 1,800 litres are still wanted. From then on the net gain is 150 − 60 = 90 litres a minute, needing 1,800 ÷ 90 = 20 minutes; the cistern fills at 6:32 a.m. 6:24 a.m. ignores the drain altogether (3,600 ÷ 150). 6:40 a.m. treats the drain as open from 6:00 (3,600 ÷ 90). 6:52 a.m. gets the net rate right but divides the whole 3,600 litres by it and then adds the first 12 minutes as well, counting the opening stretch twice.