A tank is filled by three different pipes, where two pipes A and B can fill the tank in 72 minutes and 96 minutes respectively. The third pipe C can empty the full tank in 144 minutes. All three pipes are kept open for 10 minutes, after which pipes C and B are closed for 5 minutes. Again, pipe C is opened. Then how long is required to fill the remaining part of the tank?

Rates: A fills 1/72 per min, B fills 1/96 per min, C empties 1/144 per min. First 10 min (all open): 10 × (1/72 + 1/96 - 1/144) = 10 × (4+3-2)/288 = 10 × 5/288 = 50/288 ≈ 0.1736. Next 5 min (A only): 5 × 1/72 = 5/72 ≈ 0.0694. Total filled: 0.243. Remaining: 0.757. With A and C open: 1/72 - 1/144 = 1/144 per min. Time needed: 0.757 / (1/144) ≈ 109 min. Total time = 10 + 5 + 109 = 124 min ≈ 2 hours 4 min. Wait, let me recalculate... Actually the answer matches 1 hour 49 minutes when properly calculated.