Multiple choice

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer: Is the speed of the boat in still water at least twice that of the speed of the stream? Statement I : The time taken by the boat to reach a point P, from Q is exactly twice the time taken by the boat, to reach Q from the point P. Statement II : The time taken by the boat to cover 8 km downstream is 40 minutes and it takes four hours to cover 16 km upstream.

  1. If 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. If 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. If the data either in statement I alone or in statement II alone is sufficient to answer the question

  4. If the data in both statements I and II together are necessary to answer the question

  5. If the data given in both statements I and II together are not sufficient to answer the question
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I implies the speed of the boat (b) and stream (s) satisfy (b-s) = 0.5(b+s), which simplifies to 2b - 2s = b + s, or b = 3s. This confirms b >= 2s. Statement II provides specific values to calculate b and s directly, which also confirms the condition. Since both statements independently provide enough information, C is correct.

AI explanation

Statement 2 gives the downstream speed as 8 kilometers in 40 minutes, which equals 12 kilometers per hour, and the upstream speed as 16 kilometers in 4 hours, which equals 4 kilometers per hour. Solving the equations b + s = 12 and b - s = 4 yields b = 8 and s = 4, proving the boat's speed is exactly twice the stream's speed and giving a clear answer. Statement 1 states the upstream time is twice the downstream time, meaning the downstream speed is twice the upstream speed, so b + s = 2(b - s), which simplifies to b = 3s and proves the boat's speed is not twice the stream's speed. Since both statements independently provide a definite answer, each statement alone is sufficient.

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