Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement (s) is/are necessary to answer the questions. What is the speed of the current? (R.B.I., 2004) I. Speed of the boat is 4 km/hr in still water. II. The boat runs at a speed of 6 km/hr downstream. III. The difference between the speeds of the boat while travelling in still water and downstream is 2 km/hr.

### Concept & Speed Relationships The speed of a boat downstream is the sum of its speed in still water and the speed of the current. $$Speed_{downstream} = Speed_{still} + Speed_{current}$$ ### Step-by-Step Solution * Let the speed of the boat in still water be $u$ and the speed of the current be $v$. We need to find $v$. * From Statement I: $u = 4$ km/hr. This alone is not sufficient. * From Statement II: $u + v = 6$ km/hr. This alone is not sufficient. * From Statement III: The difference between downstream speed and still water speed is given. Downstream speed is $u + v$. So, $(u + v) - u = 2 \Rightarrow v = 2$ km/hr. Statement III alone is sufficient to find the speed of the current. * Combining Statements I and II: Substitute $u = 4$ into $u + v = 6$. This gives $4 + v = 6 \Rightarrow v = 2$ km/hr. Statements I and II together are also sufficient. * Therefore, the data in Statement III alone is sufficient, OR the data in Statements I and II together are sufficient. ### Exam Strategy & Shortcut Statement III directly defines the speed of the current in words. The "difference between downstream speed and still water speed" is exactly the speed of the current. Recognizing this definition immediately shows Statement III is sufficient on its own. ### Common Pitfall A common pitfall is stopping after realizing I and II work together, thereby incorrectly choosing "Only I and II" and ignoring that Statement III mathematically yields the answer independently. ### Final Answer Therefore, the correct answer is **Either I and II together or only III**.