Multiple choice

Directions: In this problem, a question is given followed by three statements numbered (I), (II) and (III). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question. At what speed can the man swim in still water? I. The man can swim 15 km downstream in 3 hours. II. He can swim 5 km upstream in 5 hours. III. Speed of the man is 50% more than the speed of current.

  1. Only statements I and II

  2. Only statements II and III

  3. Any two statements

  4. All three statements

  5. Only statement III and either statement I or statement II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let m be man's speed and c be current speed. I: m+c = 15/3 = 5. II: m-c = 5/5 = 1. III: m = 1.5c. With any two statements, we have two equations with two variables, which is sufficient to solve for m.

AI explanation

Statements one and two provide the downstream speed as 5 km/hr and the upstream speed as 1 km/hr, allowing us to calculate still water speed using the formula half of the sum of downstream and upstream speeds, which equals 3 km/hr. Statements one and three can be combined by letting the man's speed be 1.5 times the stream speed to solve the downstream equation, yielding the same result. Statements two and three can similarly be combined using the upstream equation to find the same speeds. Therefore, any two of the three statements are sufficient to answer the question.

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