Multiple choice

Passage

Directions: Study the paragraph and answer the question that follows. There were two similar tanks X and Y with five similar pipes P, Q, R, S and T. Pipes P, Q and R can fill the empty tank in 10 minutes, 15 minutes and 30 minutes respectively, while pipes S and T can empty the filled tank in 20 minutes and 30 minutes respectively. Tank X had no leaks, but tank Y had a leak, such as when pipe P was opened in the empty tank Y, it took 12 minutes to fill tank Y.

If pipe Q was opened into the empty tank Y, it could be filled in ______ minutes, while pipe R could fill the empty tank Y in _______ minutes. Which of the following options satisfies the two blanks in the question? A. 16, 32 B. 16, 48 C. 20, 60 D. 20, 80

  1. Only A

  2. Only B

  3. Only C

  4. Only D

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Pipe P fills tank X in 10 min. In tank Y, it takes 12 min, implying a leak rate L = 1/10 - 1/12 = 1/60. Pipe Q fills in 15 min, so net rate in Y is 1/15 - 1/60 = 3/60 = 1/20 (20 min). Pipe R fills in 30 min, so net rate in Y is 1/30 - 1/60 = 1/60 (60 min).

AI explanation

First find the leak rate by comparing tank Y to tank X using pipe P. The leak's rate is 1/10 minus 1/12, which equals 1/60 per minute. When only pipe Q works with the leak, the net rate is 1/15 minus 1/60, which equals 3/60 or 1/20 per minute, taking 20 minutes to fill. When only pipe R works with the leak, the net rate is 1/30 minus 1/60, which equals 1/60 per minute, taking 60 minutes to fill. This matches the pair 20, 60 given in option C.

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