Multiple choice

Directions: The item given below consists of a question and two statements, numbered I and II. You have to decide whether the data provided in the statement is sufficient to answer the question. Read both the statements and choose the correct option. What is the time taken by pipe C to fill the water tank alone if the time taken by pipe A to fill the water tank is 12 minutes? I. Time taken by pipes A, B and C to fill the water tank together is 6 minutes. II. The ratio of speed of water that comes through pipe B to that of the water that comes out of pipe C is 4 : 3.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. The data in both statement I and II together is necessary to answer the question.

  5. The data even in both statements I and II together is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the combined rate (A+B+C). Statement II gives the ratio of rates for B and C. With A known, we have two equations with two variables (B and C), allowing us to solve for C.

AI explanation

Let the filling rates of pipes A, B and C be a, b and c, and statement 1 gives the combined equation a + b + c = 1/6. Statement 2 gives the ratio of the rates for B and C as 4 to 3, meaning b = (4/3)c. Since pipe A takes 12 minutes to fill the tank alone, its rate is a = 1/12. Substituting this into the first equation gives 1/12 + (4/3)c + c = 1/6, which simplifies to (7/3)c = 1/12 and yields c = 1/28, meaning pipe C takes 28 minutes alone. Both statements together are necessary to find the time taken by pipe C.

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