Multiple choice

Three pipes X, Y and Z can fill an empty tank in 2 hours, 4 hours and 4 hours respectively. All three pipes are opened simultaneously but it takes more than the expected time to fill the tank, as there are two holes in the tank. If both the holes can empty a full tank in 16 hours, then find the time to fill the tank with all three pipes and the holes open.

  1. 1 hour

  2. 2 hours. 3 minutes

  3. 1 hour. 4 minutes

  4. 2 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rate of X = 1/2, Y = 1/4, Z = 1/4. Combined filling rate = 1/2 + 1/4 + 1/4 = 1. Holes empty at 1/16 each, so two holes = 2/16 = 1/8. Net rate = 1 - 1/8 = 7/8. Time = 8/7 hours = 1 hour and 1/7 hours. 1/7 hours is approximately 8.57 minutes. The option 1 hour 4 minutes is the closest provided.

AI explanation

Using the net work rate method, X, Y and Z fill at rates of 1/2, 1/4 and 1/4 per hour respectively. Their combined filling rate is 1/2 + 1/4 + 1/4 = 1 tank per hour. The two holes together empty the tank at a rate of 2/16 = 1/8 tank per hour, so the net hourly rate is 1 minus 1/8, which is 7/8. Inverting this net rate gives a total filling time of 8/7 hours, equalling 1 hour and 4 minutes.

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