A cistern can be filled by two pipes. A and B in 12 minutes and 14 minutes respectively and can be emptied by a third pipe C in 8 minutes. If all the taps be turned on at the same moment, what part of cistern will remain unfilled at the end of 7 minutes?

5/24
19/24
7/24
17/24

Correct Answer: 19/24

Explanation:

Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes
∴ In 7 minutes 5/168 x 7 = 5/24 part of the tank will be filled
∴ Requied answer = 1 - 5/24 = 19/24 part

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