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? (Bank P.O., 2007) I. Speed of the current is 2 kmph. II. Time taken by the boat to cover a distance of 24 km running upstream is one hour more than the time taken to cover the same distance running downstream.

### Concept & Time Difference Equation When a problem provides the difference in times taken for an upstream and downstream journey over a fixed distance, we set up a time equation. $$Time_{upstream} - Time_{downstream} = Time\ Difference$$ $$\frac{Distance}{u - v} - \frac{Distance}{u + v} = \Delta t$$ ### Step-by-Step Solution * Let the boat's speed in still water be $u$. * From Statement I: Current speed $v = 2$ kmph. This alone is insufficient to find the boat's speed. * From Statement II: $\frac{24}{u-v} - \frac{24}{u+v} = 1$. This equation contains two variables, making it insufficient on its own. * Combining both statements: Substitute $v=2$ into the equation from Statement II. * $\frac{24}{u-2} - \frac{24}{u+2} = 1$ * $24 \times [\frac{(u+2) - (u-2)}{u^2 - 4}] = 1 \Rightarrow 24 \times \frac{4}{u^2 - 4} = 1$ * $96 = u^2 - 4 \Rightarrow u^2 = 100 \Rightarrow u = 10$. * We can uniquely determine the speed of the boat. ### Exam Strategy & Shortcut Whenever you have a time-difference equation with distance provided (Statement II), you need one of the two speeds (boat or stream) to solve for the other. Statement I provides the stream speed, making the combination perfectly sufficient. You don't have to solve for $u = 10$ during the exam. ### Common Pitfall A frequent error is mistaking the order of the terms in the time difference equation. Since upstream speed is slower, the time taken upstream is *greater*, so it must be $Time_{upstream} - Time_{downstream}$. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**.