Multiple choice

Which information is/are sufficient to answer the questions asked? A boat covers 24 km upstream and 36 km downstream in 6 hours. What is the velocity of current? I. Speed of boat in still water is 10 km/hr. II. Boat covers 36 km upstream and 24 km downstream in 6.5 hours. III. The boat covers 48 km upstream in 6 hours and downstream in 4 hours.

  1. I or II only

  2. II or III only

  3. II and (I or III)

  4. Any one is sufficient

  5. None of these

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the given data: 24 km upstream + 36 km downstream in 6 hours. Let boat speed = b, current speed = c. We have 24/(b-c) + 36/(b+c) = 6. Statement I: b = 10 km/hr gives 24/(10-c) + 36/(10+c) = 6, which solves to c = 2 km/hr - sufficient alone. Statement II: 36 km upstream + 24 km downstream in 6.5 hours gives a second equation, making two equations in two variables (b, c) - sufficient alone. Statement III: 48 km upstream in 6 hours means b-c = 8 km/hr; 48 km downstream in 4 hours means b+c = 12 km/hr. Solving gives c = 2 km/hr - sufficient alone. Each statement independently determines the current velocity.