Two taps A and B can fill a tank with water in 20 minutes and 15 minutes, respectively. A third tap C can empty the full tank in 6 minutes. After the taps A and B fill the tank for 5 minutes, the tap C is opened to empty while A and B continue to fill it.

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Q: 1 (CAPF/2024)
Two taps A and B can fill a tank with water in 20 minutes and 15 minutes, respectively. A third tap C can empty the full tank in 6 minutes. After the taps A and B fill the tank for 5 minutes, the tap C is opened to empty while A and B continue to fill it. In how many minutes after the start shall the tank get empty?

question_subject: 

General Knowledge

question_exam: 

CAPF

The combined rate of A and B filling the tank is 1/20 + 1/15 = 7/60 of the tank per minute. After 5 minutes, A and B fill 35/60 or 7/12 of the tank. The rate of C emptying is 1/6 per minute. The net rate with C open is (7/60 - 10/60 = -1/60) of the tank per minute. To empty the remaining 5/12, it takes (5/12) / (1/60) = 25 minutes, totaling 30/60 or 1/2 of the tank in 30 minutes, equivalent to 10 4/5 minutes total.