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Data Sufficiency: Boat Speed in Still Water

XAT 2023 · Quantitative Ability & Data Interpretation · Medium · Data Sufficiency

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The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.

Rahim is riding upstream on a boat, from point A to B, at a constant speed. The distance from A to B is 30 km. One minute after Rahim leaves from point A, a speedboat starts from point A to go to point B. It crosses Rahim's boat after 4 minutes. If the speed of the speedboat is constant from A to B, what is Rahim's speed in still water?

  1. The speed of the speedboat in still water is 30 km/hour.
  2. Rahim takes three hours to reach point B from point A.
  1. A.

    Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient

  2. B.

    Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient

  3. C.

    Each statement alone is sufficient

  4. D.

    Both statements together are sufficient, but neither of them alone is sufficient

  5. E.

    Statements 1 & 2 together are not sufficient

Answer

D

Explanation

Let Rahim's speed in still water be aa, speedboat speed bb, river stream cc. Upstream speeds: a−ca-c and b−cb-c. Distance equal: 5(a−c)=4(b−c)  ⟹  a−cb−c=455(a-c) = 4(b-c) \implies \frac{a-c}{b-c} = \frac{4}{5}. To solve for aa, we need two equations for bb and cc, which requires both statements together.

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