Multiple choice

A cistern has a leak which would empty it in $8$ hours. A tap is turned on which admits $6$ litres a minute into the cistern and is now emptied in $12$ hours. How many litres does the cistern hold?

  1. $8640$
  2. $8500$
  3. $4320$
  4. $60\ hours$
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A Correct answer
Explanation

Let the capacity be C. The leak empties at C/8 per hour. With the tap adding 6 liters/min (360 liters/hour), the net rate is C/12. So, C/8 - 360 = C/12. Solving for C: C/8 - C/12 = 360, which simplifies to C/24 = 360, so C = 8640 liters.

AI explanation

Let the leak rate be y litres per hour, so the equation for the net emptying rate is y minus 360 litres per hour equals the tank capacity divided by 12 hours. Because the tank capacity is 8y litres, the equation becomes y minus 360 equals 8y divided by 12. Solving this gives y equal to 1080 litres per hour, making the total capacity 8640 litres.

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