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If Tank is full with Pipe A in 15 minutes and empty from Pipe B and C in 40 minutes and 45 minutes respectively, how much time will it take to fill the tank if all pipes are open while the tank is 2/9 full?
  1. 25 minutes
  2. 30 minutes
  3. 35 minutes
  4. 40 minutes
Explanation
  • Pipe A fills the tank in 15 minutes, so its filling rate is 1/15 of the tank per minute.
  • Pipe B empties the tank in 40 minutes, so its emptying rate is 1/40 of the tank per minute.
  • Pipe C empties the tank in 45 minutes, so its emptying rate is 1/45 of the tank per minute.
  • The combined rate of filling and emptying is: Rate=115−(140+145)text{Rate} = frac{1}{15} - left(frac{1}{40} + frac{1}{45}right) Simplifying the rates and calculating the time required to fill the remaining part (7/9 of the tank) gives 40 minutes.

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