Three pipes A, B and C can fill a tank in 12 hours, 20 hours and 30 hours respectively. All the three pipes are opened together, after some hours pipe A is closed. After another 3 hours, pipe B is closed and pipe C fills the remaining tank in 15 hours. What was the total time taken to fill the tank?

Let A, B, C work together for x hours. Work done in x hours: x(1/12 + 1/20 + 1/30) = x(20/240). Then A closes, B and C work for 3 hours: 3(1/20 + 1/30) = 3(5/60) = 1/4. Remaining work by C in 15 hours: 15/30 = 1/2. Total work = x/12 + 1/4 + 1/2 = 1. Solving: x/12 = 1/4, so x = 3 hours. Total time = 3 + 3 + 15 = 19.5 hours. Check: 3(20/240) + 1/4 + 1/2 = 1.