Multiple choice

Three pipes A, B and C are connected to a tank. Out ofthe three, A and B are the inlet pipes and C is the outletpipe. If opened separately, A fills the tank in 10 hoursand B fills the tank in 30 hours. If all three are openedsimultaneously, it takes 30 minutes extra than if only Aand B are opened. How much time does it take toempty the tank if only C is opened?

  1. 140 Hours

  2. 100 Hours

  3. 200 Hours

  4. 120 Hours

  5. 160 Hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rate of A = 1/10, Rate of B = 1/30. Combined rate (A+B) = 1/10 + 1/30 = 4/30 = 2/15. Time for A+B = 15/2 = 7.5 hours. Combined rate (A+B-C) = 1/(7.5 + 0.5) = 1/8. So, 2/15 - Rate C = 1/8. Rate C = 2/15 - 1/8 = (16-15)/120 = 1/120. Thus, C empties the tank in 120 hours.

AI explanation

Using the combined work formula, pipes A and B fill 1/10 + 1/30 = 4/30, or 2/15 of the tank per hour, meaning they can fill it in 7.5 hours. With pipe C open, the process takes 30 minutes more, so the time is 8 hours, making the combined rate of all three pipes 1/8 per hour. The emptying rate of pipe C is the difference between the rate of A and B and the rate of all three pipes, which is 2/15 - 1/8 = 1/120 per hour. Therefore, pipe C alone takes 120 Hours to empty the tank.

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