Pipe A can fill the tank in 8 hours and pipe B can fill the same tank in 12 hours. When the tank is 50\% filled, the third pipe C opens up which can empty the tank in 6 hours. After how many hours will the tank be completely filled?

Pipes A and B together fill at rate 1/8 + 1/12 = 5/24 per hour. First 50% takes (1/2) / (5/24) = 12/5 = 2.4 hours (2 hours 24 minutes). When C opens, net rate becomes 5/24 - 1/6 = 1/24 per hour. Remaining 50% takes (1/2) / (1/24) = 12 hours. Total = 14 hours 24 minutes. Option A (8h 40m) assumes C opens from start; Option D (8h 24m) miscalculates the two-phase filling.