Multiple choice

Directions: The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and mark the correct answer. What is the speed of the boat in still water? (in kmph) I. The boat takes total time of 4 hours to travel 14 km upstream and 35 km downstream together. II. The boat takes total time of 5 hours to travel 29 km upstream and 24 km downstream together.

  1. The data in statement (I) alone is sufficient to answer the question].

  2. The data in statement (II) alone is sufficient to answer the question.

  3. The data in both the statements together is needed.

  4. Either statement (I) alone or statement (II) alone suffices to answer the question.

  5. Even by combining both the statements the answer can not be found.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u be the upstream speed and v the downstream speed. Each statement gives one equation involving both speeds, so neither alone is sufficient. Together, the two independent equations determine the speeds and hence the still-water speed.

AI explanation

Let the boat's speed in still water be u and the stream's speed be v, giving downstream and upstream speeds of (u + v) and (u - v). Statement I provides the equation 35 / (u + v) + 14 / (u - v) = 4, and statement II provides 24 / (u + v) + 29 / (u - v) = 5. Neither equation alone can solve for the two variables, but treating 1 / (u + v) and 1 / (u - v) as two unknowns shows that both equations together form a solvable simultaneous system.

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