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Pipe A fills a tank in 20 minutes, pipe B in 30 minutes, and pipe C empties it in 15 minutes. They are opened one at a time for a minute each in the order A, B, C, A, B, C, … on the empty tank. When is the tank first full?

Competition practicePipes & Cisterns
  • A165 min
  • B168 min
  • C167 min
  • D180 min

Step-by-Step Solution

One 3-minute cycle: . After 55 cycles (165 min) the tank holds ; A adds and B , making it full at 167 min. (180 min forgets the tank fills before C's turn.)
Answer: C) 167 min

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