Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the speed of the boat in still water? I. The speed downstream of the boat is thrice the speed upstream. II. The sum of the speeds of the boat, upstream and downstream is 12 kmph.

### Concept & Speed Relations The fundamental formula connecting still water speed with upstream and downstream speeds is a simple average. $$Speed\ in\ still\ water = \frac{Speed_{downstream} + Speed_{upstream}}{2}$$ ### Step-by-Step Solution * Let downstream speed be $D$ and upstream speed be $U$. * From Statement I: $D = 3U$. This is a ratio. We cannot find the exact speed in still water. Thus, I alone is not sufficient. * From Statement II: We are given $D + U = 12$ kmph. * We know that Speed in still water = $\frac{D + U}{2}$. * Substituting the given sum: Speed in still water = $\frac{12}{2} = 6$ kmph. * Statement II alone gives us the exact answer directly. ### Exam Strategy & Shortcut Always look closely at what formulas define your target variable. If the target is $\frac{D+U}{2}$, and a statement directly gives you the value of $(D+U)$, you can instantly solve it without finding $D$ and $U$ individually. ### Common Pitfall A common pitfall is overcomplicating the problem by trying to use Statement I to find the individual downstream and upstream speeds before realizing Statement II gives you everything you need in a single piece. ### Final Answer Therefore, the correct answer is **if the data in Statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question;**.