Pipe A fills a tank of $700$ litres capacity at the rate of $40$ litres a minute. Another pipe B fills the same tank at the rate of $30$ litres a minute. A pipe at the bottom of the tank drains the tank at the rate of $20$ litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

Pipe A fills at 40 liters per minute, pipe B fills at 30 liters per minute, and pipe C drains at 20 liters per minute. In a three-minute cycle, the net fill is 40 + 30 - 20 = 50 liters, so for a 700-liter tank this takes 14 cycles. Each cycle takes 3 minutes, so 14 cycles take 42 minutes.

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