A boat takes 2 hours to travel from point A to point B in still water. You want to find the speed of the boat when it is travelling upstream. Which of the following pieces of information are required? A. Distance between points A and B. B. Time taken to travel downstream from B to A. C. Speed of the stream of water.

Introduction / Context:
This question is about data sufficiency in a boats and streams setting. You are told how long a boat takes to travel between two points in still water, and asked which additional pieces of information are needed to determine the upstream speed. Rather than calculating a numeric value, you must analyse which combinations of given data would make that computation possible.

Given Data / Assumptions:

• Time taken from A to B in still water = 2 hours.
• Let distance between A and B be D km.
• Let speed of boat in still water be b km/h and speed of stream be s km/h.
• Upstream speed = b - s, downstream speed = b + s.
• Statements:
  • A: Distance between A and B (value of D).
  • B: Time taken to travel downstream from B to A.
  • C: Speed of the stream s.

Concept / Approach:
From the still water information, we know that D = b * 2, so D = 2b. This relationship links distance and still water speed. We need to decide which combinations of A, B and C allow us to find b and s and hence compute b - s, the upstream speed. The key is to see that any two of A, B and C, together with the still water time, are sufficient to determine b and s uniquely.

Step-by-Step Solution:
Case 1 (A and B): If we know distance D and downstream time t_down from B to A, we can find downstream speed = D / t_down. From the still water time, D = 2b, so b = D / 2. Then downstream speed = b + s = D / t_down. This gives s = D / t_down - b, so we can find b - s, the upstream speed. Thus A and B are sufficient. Case 2 (B and C): Knowing downstream time t_down and stream speed s, we know that downstream speed = D / t_down = b + s. From the still water relation, D = 2b. So D / t_down = 2b / t_down = b + s. This is an equation in b because s and t_down are known, allowing us to solve for b and then compute b - s. Thus B and C are also sufficient. Case 3 (C and A): Knowing D and s, we have b = D / 2 from still water and can immediately compute upstream speed = b - s.

Verification / Alternative check:
In every case above, once b and s are known, upstream speed b - s is fully determined. There is no scenario where all three A, B and C are simultaneously necessary; any pair provides enough information. Therefore, the correct logical conclusion is that any one pair among (A, B), (B, C) or (C, A) is sufficient.

Why Other Options Are Wrong:
Option stating “Only A and B” ignores that B and C together or C and A together also work. Option “Only B and C” similarly neglects other valid pairs. Saying “All are required” is too strong, because we have already shown each pair is sufficient. “Only A and C” incorrectly rules out B and C as a sufficient combination.

Common Pitfalls:
Many learners mistakenly think distance is always essential, or they assume that without all three pieces of data the problem is unsolvable. The key insight is to express D in terms of b using the still water time and then see how each extra statement supplies enough information to determine the unknowns. Practising this type of logical reasoning is crucial for data sufficiency questions.

Final Answer:
Any one pair of A and B, B and C, or C and A is sufficient to determine the upstream speed.