Multiple choice

A cistern is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the tap that is filling the tank is turned off, then how much time will it take the leak take to empty the tank, if it is completely filled.

  1. 14

  2. 28

  3. 16

  4. 22

  5. 40
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the tank capacity be 1 unit. Normal fill rate = 1/8 per hour. With leak, fill rate = 1/10 per hour (takes 10 hours). The leak empties at rate = (1/8 - 1/10) = (5-4)/40 = 1/40 per hour. If the tap is turned off and tank is full, the leak alone would take 40 hours to empty it (1 / (1/40) = 40).

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