Multiple choice

Directions: Answer the question independently. A tank has three pipes—Pipe A, Pipe B and Pipe C attached. Pipe A and Pipe C alone can fill the tank completely in 4 hours and 8 hours respectively. Pipe B can empty the tank in 6 hours. Initially the tank is empty. The three pipes are operated in the following sequence. In the first hour, only pipe A is opened. In the second hour, pipes A and B are opened. In the third hour, only pipe B is opened. In the fourth hour, pipes B and C are opened. In the fifth hour, only pipe C is opened. This cycle of 5 hours is repeated. After how many hours will the tank be completely filled for the first time?

  1. 1.5 hours

  2. 18 hours

  3. 20 hours

  4. 16 hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rates: A = +1/4, B = -1/6, C = +1/8. Cycle (5 hours): Hr 1: +1/4. Hr 2: +1/4 - 1/6 = +1/12. Hr 3: -1/6. Hr 4: -1/6 + 1/8 = -1/24. Hr 5: +1/8. Net per cycle = 1/4 + 1/12 - 1/6 - 1/24 + 1/8 = (6+2-4-1+3)/24 = 6/24 = 1/4. After 3 cycles (15 hours), tank is 3/4 full. Hr 16: +1/4. Total = 1. Tank is full at 16 hours.

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