Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to permanent leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If A and B opens for 5 hours then closed, in what time would the leak empty it?

Pipe A rate = 1/12 per hour, Pipe B rate = 1/20 per hour. Combined rate = 1/12 + 1/20 = 8/60 = 2/15 tank per hour, so they should fill in 7.5 hours normally. But with leak, they take 8 hours (30 min extra). Actual rate with leak = 1/8 per hour. Leak rate = 2/15 - 1/8 = 1/120 per hour (empties). After pipes fill for 5 hours: 5 × (2/15) = 2/3 tank filled. Leak empties at 1/120 per hour, so to empty 2/3 tank: (2/3)/(1/120) = 80 hours. Option D claims 80 but the leak would empty a FULL tank in 120 hours, not 75.