A cistern is provided with two pipes A and B. A can fill it in 20 minutes. A and B can empty it in 30 minutes. If A and B are kept open alternatively for one minute each, how soon will the cistern be filled?

A fills at 1/20 per minute. A+B empty at 1/30 per minute, so B empties at 1/30 - 1/20 = -1/60 per minute (negative = emptying). Alternate operation: minute 1 (A fills): 1/20, minute 2 (B empties): 1/20 - 1/60 = 1/30. Net every 2 minutes = 1/30. After 118 minutes: 59/30, which exceeds capacity. Let me recalculate properly: In 2-minute cycles, net = 1/60 filled. After 118 minutes (59 cycles): 59/60 filled. At minute 119 (A fills): 59/60 + 1/20 = 62/60 (overfills). So actual completion at 120 minutes.