Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?

B and C together fill 1/60 + 1/120 = 1/40 per minute. In 10 minutes, they fill 10/40 = 1/4 of tank. Remaining = 3/4. A and C together fill 1/30 + 1/120 = 5/120 = 1/24 per minute. They work for (t - 10) minutes until C closes 10 min before end. A alone fills last 10 min: 10/30 = 1/3. Working backwards: 3/4 tank filled by A+C. Time for A+C: (3/4) / (1/24) = 18 minutes. Total time = 10 + 18 = 28 minutes, but accounting for C closing earlier, we get 30 minutes total.