Two pipe A, B can fill a tank in 30 and 15 hours whereas a third pipe can empty it in 12 hours. If all the pipes are open alternatively starting by A and followed by B and C. Find in how many hours the tank will be filled?

A fills 1/30 per hour, B fills 1/15 per hour, C empties 1/12 per hour. Net fill per 3-hour cycle (A then B then C) = 1/30 + 1/15 - 1/12 = (2+4-5)/60 = 1/60. After 486 hours (162 cycles), tank is 486/60 = 8.1 full (overflow). Starting from empty: after 162 cycles = 483 hours, tank has 162/60 = 2.7. Hour 484 (A): 2.7 + 1/30 = 2.733. Hour 485 (B): 2.733 + 1/15 = 2.8. Hour 486 (C): 2.8 - 1/12 = 2.717. Need total of 1. After 164 hours (54 cycles + 2 hours): 54/60 + 1/30 + 1/15 = 0.9 + 0.033 + 0.067 = 1.0. So 164 hours (Option B).