Multiple choice

Passage

Directions: The following question is accompanied by three statements - (A) or (I), (B) or (II) and (C) or (III). You have to determine the statement(s) which is/are sufficient/necessary to answer the question.

What is the speed of the stream? A. The boat covers 80 km in 20 hours moving upstream. B. The boat covers 80 km in 10 hours moving downstream. C. The ratio between the speeds of the boat and the stream is 6 : 2, respectively.

  1. Only A and B together are sufficient.

  2. Any two of the three statements are sufficient.

  3. Only A and C together are sufficient.

  4. Only B and C together are sufficient.

  5. All A, B and C together are required.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A: Upstream speed = 80/20 = 4 km/hr. B: Downstream speed = 80/10 = 8 km/hr. C: Ratio of boat speed (b) to stream speed (s) is 6:2, or 3:1. With A and B, b-s=4 and b+s=8, so 2b=12, b=6, s=2. With A and C, b-s=4 and b/s=3, so 3s-s=4, 2s=4, s=2. With B and C, b+s=8 and b/s=3, so 3s+s=8, 4s=8, s=2. Any two statements are sufficient.

AI explanation

Using the upstream and downstream speed formulas, upstream speed equals the boat speed minus the stream speed and downstream speed equals the boat speed plus the stream speed. Statements A and B together give an upstream speed of 80 divided by 20, or 4 km/hr, and a downstream speed of 80 divided by 10, or 8 km/hr, which allows you to solve for the stream speed as (8 - 4) divided by 2, giving 2 km/hr. Statements A and C together provide the upstream speed of 4 km/hr and a boat to stream ratio of 6 to 2, allowing you to solve the equation boat speed minus stream speed equals 4 to find the stream speed is 2 km/hr, while statements B and C together provide the downstream speed of 8 km/hr and the same ratio to find the stream speed is 2 km/hr. Any two of the three statements are sufficient to find the speed of the stream, so any two of the three statements are sufficient.

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