Multiple choice

What is the speed of the boat in still water? Statement I: To travel 32km in upstream and 36km in downstream it takes a total of 7 hours. Statement II: Time taken to travel 54km in downstream is 150min less than time taken to travel 56km in upstream. Statement III: Speed in upstream is 33.33% less than speed in downstream.

  1. I and either II or III

  2. Any two

  3. III and either I or II

  4. II and III

  5. None of these

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

Let boat speed = b, stream speed = s. Downstream speed = b+s, upstream = b-s. Statement I: 32/(b-s) + 36/(b+s) = 7. Statement II: 54/(b+s) + 56/(b-s) - 54/(b+s) = 2.5, which simplifies to 56/(b-s) - 54/(b+s) = 2.5. Statement III: b-s = (2/3)(b+s), so b = 5s. Using I and III together: From III, substitute b = 5s in I to get two equations in two variables, solving gives s = 1.5, b = 7.5. Using II and III: Same approach gives s = 1.5, b = 7.5. Using I and II: Solving simultaneously gives b = 7.5 or 13.5, ambiguous. Any two statements suffice if we pick the right pair.