Multiple choice

Passage

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What is the ratio of the speed of boat in still water to the speed of stream? I. A boat went downstream for 120 km and immediately returned and it took the boat 15 hours to complete the round trip. II. A boat went downstream for 96 km and immediately returned and it took the boat 12 hours to complete the round trip. III. If the speed of the river was twice as high, the trip downstream and back would take 12 hours.

  1. All I, II and III together are sufficient

  2. Both II and III together are sufficient

  3. Either I and III or II and III together are sufficient

  4. Both I and II together are sufficient

  5. Both I and III together are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u be boat speed and v be stream speed. Round trip time = d/(u+v) + d/(u-v). With two equations (I and II), we have two variables (u, v) and the ratio d is known, but we need the ratio u/v. Statement III provides a third scenario to solve for the ratio.

AI explanation

Let the boat's speed in still water be B and the stream's speed be S; statement (1) yields the equation 120 divided by the quantity B plus S, plus 120 divided by the quantity B minus S, equals 15. Combining this with statement (3) gives a second equation where 120 divided by the quantity B plus 2S, plus 120 divided by the quantity B minus 2S, equals 12, creating a solvable system for the ratio of B to S. Similarly, statement (2) gives the base equation 96 divided by the quantity B plus S, plus 96 divided by the quantity B minus S, equals 12, which also forms a solvable system when paired with statement (3). Consequently, either statements I and III or statements II and III together are sufficient.

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