Two entrance pipes can fill a tank in 10 and 12 hours respectively and one drainage pipe can empty 80 gallons of water per hour. All the three pipes working together can fill an empty tank in 20 hours. What is the capacity (in gallons) of the tank?

Let the tank capacity be C gallons. The two inlet pipes fill at C/10 and C/12 gallons per hour. The drainage pipe empties 80 gallons/hour. Working together, their net rate is (C/10 + C/12 - 80) gallons/hour. Since they fill the tank in 20 hours: C/20 = C/10 + C/12 - 80. Solving: C/20 = 11C/60 - 80, so 3C = 11C - 4800, giving 8C = 4800, hence C = 600 gallons.