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.

When pipes Q and S were simultaneously opened into the empty tank X, 40 gallons of liquid was filled in the tank after 12 minutes. This means that the tank had a capacity of _____ gallons and pipe S could empty it at a rate of _______ gallons per minute. Which of the following options satisfies the two blanks in the question? (A) 200, 10 (B) 240, 12 (C) 280, 15 (D) 320, 20

  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
A Correct answer
Explanation

P fills in 10, Q in 15, R in 30. S empties in 20. Rate of Q = 1/15, Rate of S = -1/20. Net rate = 1/15 - 1/20 = 1/60. In 12 minutes, 12/60 = 1/5 of the tank is filled. If 1/5 capacity = 40 gallons, then capacity = 200 gallons. Pipe S rate = 1/20 of 200 = 10 gallons/min.

AI explanation

The rates for pipes Q and S are found by taking the reciprocal of their respective times, meaning pipe Q fills at 1/15 of the tank per minute and pipe S empties at 1/20 of the tank per minute. When opened together, their combined net rate is 1/15 minus 1/20, which equals 1/60 of the tank per minute. Multiplying this net rate by 12 minutes shows that 12/60, or 1/5, of the tank is filled by the 40 gallons of liquid. The total capacity is therefore 5 times 40, resulting in 200 gallons. Since pipe S empties 1/20 of this 200-gallon capacity per minute, it empties at a rate of 10 gallons per minute, which corresponds to option A.

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