Multiple choice

Two pipes A and B can fill a tank in 36 minutes and 45 minutes, respectively. Another pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. Total time taken for the tank to be filled up is

  1. 49 minutes

  2. 46 minutes

  3. 45 minutes

  4. 39 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A fills 1/36 per min, B fills 1/45 per min, C empties 1/30 per min. A+B fill (1/36 + 1/45) = 9/180 = 1/20 per min. In 7 mins, they fill 7/20. Remaining = 13/20. Then A+B-C = 1/36 + 1/45 - 1/30 = (5+4-6)/180 = 3/180 = 1/60. Time for remaining = (13/20) / (1/60) = 39 mins. Total = 7 + 39 = 46 mins.

AI explanation

Using the one-day work method, the filling rates of pipes A and B are 1/36 and 1/45 respectively, and the emptying rate of pipe C is 1/30. In the first 7 minutes, pipes A and B fill 7 * (1/36 + 1/45) = 7 * (9/180) = 7/20 of the tank, leaving 13/20 of the tank to be filled. When C is opened, the net hourly work becomes (1/36 + 1/45 - 1/30) = (5 + 4 - 6)/180 = 3/180 = 1/60. The remaining 13/20 of the tank is filled at this net rate in (13/20) / (1/60) = 39 minutes. Adding the initial 7 minutes to this 39 minutes gives a total filling time of 46 minutes.

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