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Pipe 'M' can fill an empty tank in 40 minutes and pipe 'N' can empty the full tank in 50 minutes. If both pipes are opened simultaneously, in what time will it be half filled ?

  • A.2 hours, 20 minutes
  • B.1 hour, 30 minutes
  • C.3 hours, 20 minutes
  • D.1 hour, 40 minutes

Answer: D

The tank is half filled in 1 hour, 40 minutes.

Pipe M fills \(\frac{1}{40}\) of the tank per minute and pipe N empties \(\frac{1}{50}\) per minute. Together:

\[ \begin{aligned} \frac{1}{40} - \frac{1}{50} &= \frac{5 - 4}{200} \\ &= \frac{1}{200} \end{aligned} \]

So the full tank would take 200 minutes, and half the tank takes 100 minutes, which is 1 hour 40 minutes.

3 hours 20 minutes (200 minutes) is the time to fill the whole tank, the most likely slip.

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