Multiple choice

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. A boat starts from point A at 7:00 a.m. for point B. Find the distance between points A and B. Statement I: The ratio of the downstream speed to speed of the boat is 4:3 respectively. The difference between the time taken for going from point A to point B and that of the same while returning is 1 hour. Statement II: The boat reached point B at 11:00 a.m. Statement III: The speed of stream is 2 km/h.

  1. The data in statement I and statement II together are necessary to answer the question, while data in statement III alone is not sufficient to answer the question.

  2. The data in statement I and statement III together are necessary to answer the question, while data in statement II alone is not sufficient to answer the question.

  3. The data in statement II and statement III together is necessary to answer the question, while data in statement I alone is not sufficient to answer the question.

  4. Either option (a) or option (c)

  5. All the statements together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the ratio of downstream speed to boat speed, but not the actual speeds. Statement II gives the time duration (4 hours). Statement III gives the stream speed. With stream speed and the ratio from I, we can find the boat speed. With boat speed and time from II, we can find distance. Thus, I and III are needed to find the boat speed, and II is needed to find the distance.

AI explanation

From statement III, the speed of the stream is given as 2 km/h. Using the ratio from statement I, let the downstream speed be 4x and the boat's speed be 3x; since the stream speed is the difference between the boat's speed and the upstream speed, we have 2x = 2, so x = 1. This gives a downstream speed of 4 km/h and an upstream speed of 2 km/h, and since the time difference of 1 hour equals d/2 - d/4, the distance d is 4 km. Therefore, the data in statement I and statement III together are necessary, while statement II is not needed.

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