Question

A boat takes 3 hours to travel from point X to Y upstream and Y to X downstream. What is the speed of the water current in km/hour?
Statement 1: The speed of boat in still water is 6 kmph
Statement 2: In some other river, stream the boat covers the same distance in 2 hours with the same speed.

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

Answer: (E)

The problem involves determining the speed of the water current based on two given statements. Let's analyze each statement and understand why neither is sufficient to answer the question:

1. Understanding the Problem:
   • We have a boat journey upstream from point X to Y and downstream from Y to X.
   • The total time for the round trip is 3 hours.
   • We need to find the speed of the water current.
2. Statement 1: The speed of the boat in still water is 6 kmph.
   • In upstream motion, effective speed = speed of the boat in still water - speed of current.
   • In downstream motion, effective speed = speed of the boat in still water + speed of current.
   • Let the speed of the current be c kmph, and the distance for one way be d km.
   • Time upstream = \frac{d}{6-c}
   • Time downstream = \frac{d}{6+c}
   • Total time = \frac{d}{6-c} + \frac{d}{6+c} = 3 \text{ hours}
   • We have one equation with two unknowns (d and c), which is insufficient to solve for c alone.
3. Statement 2: In some other river, the boat covers the same distance in 2 hours with the same speed.
   • This statement gives the time for the boat to cover the same distance but in a different river.
   • It does not provide information about the characteristics (speed of current) of this other river.
   • Thus, this statement is not useful in determining the current speed in the river from point X to Y.
4. Conclusion:
   • Each statement alone lacks sufficient data to determine the speed of the water current. Both statements fail to provide the missing necessary data about the distance or another relation between upstream and downstream times.

Therefore, the correct answer is: Neither statement (1) nor statement (2) suffices to answer the question.