Multiple choice

Mr. Mittal has a bath tub, to which two pipes, one for hot water and one for cold water, are attached. The hot water pipe can fill the tank in 8 hr and the cold water pipe can fill the tank in 12 hr. There is an outlet pipe which can empty the tank in 6 hr. The hot water and cold water pipes are open all the time, but the outlet pipe is opened after every two hours for one hour, and then closed again for the next two hours. How much time will the bath tub take to be completely filled with water?

  1. 3 hr and 12 min

  2. 6 hr and 12 min

  3. 5 hr and 16 min

  4. 6 hr and 24 min

  5. 8 hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Hot pipe fills 1/8 per hr, cold pipe fills 1/12 per hr. Net fill rate = 1/8 + 1/12 = 5/24 per hr. With outlet open, rate = 5/24 - 1/6 = 1/24 per hr. In 3-hour cycles (2 hrs fill, 1 hr empty), net fill = (5/24 * 2) - (1/6 * 1) = 5/12 - 2/12 = 3/12 = 1/4. After 6 hours (2 cycles), tank is 1/2 full. In the next 2 hours, it fills 5/12, total 11/12. Remaining 1/12 takes (1/12) / (5/24) = 2/5 hours = 24 minutes. Total time = 6 hr + 24 min.

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