Multiple choice

Directions: The given question is followed by three statements numbered I, II and III. Read all the statements to find the answer to the given question. Choose which of the given statements is/are required to answer the question. What is the speed of the boat in still water? I. The boat can cover 15 km distance upstream in 3 hours. II. The boat can cover 30 km distance downstream in 2 hours. III. The boat can cover 30 km upstream and 15 km downstream in 7 hours.

  1. Only I

  2. Only II and III

  3. Only I and II

  4. Any two of the given three

  5. All three statements together cannot give the answer.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let u be speed upstream and v be speed downstream. Statement I gives u = 15/3 = 5 km/hr. Statement II gives v = 30/2 = 15 km/hr. Still water speed = (v+u)/2 = (15+5)/2 = 10 km/hr. Statement III also allows finding u and v. Any two statements are sufficient.

AI explanation

To find the speed of the boat in still water, we must establish the upstream and downstream speeds by solving a system of two independent linear equations. Statement I provides the equation for upstream speed (15/3 = 5 kmph), while Statement II provides the equation for downstream speed (30/2 = 15 kmph), making the combination of I and II sufficient. Furthermore, any pair of statements creates a solvable system: III with I yields the downstream speed via simultaneous equations, and III with II yields the upstream speed. Therefore, any two of the given three statements are required and sufficient to answer the question. The correct choice is Any two of the given three.

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