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 given 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. A train crosses another train running in the same direction in one minute. What is the speed of the faster train? I. The speed of the slower train is 80 kmph. II. The sum of the lengths of both the trains is 300 m.

### Concept & Formula When trains run in the same direction, their relative speed is the difference of their individual speeds. $$Time = \frac{L_1 + L_2}{S_{faster} - S_{slower}}$$ ### Step-by-Step Solution * Let the speed of the faster train be $S_f$ and the slower train be $S_s$. The time given is $t = 1$ minute $= 60$ seconds. * From Statement I: $S_s = 80$ kmph. This is insufficient without knowing the lengths of the trains. * From Statement II: $L_1 + L_2 = 300$ m. This is insufficient without knowing the speed of the slower train. * Combining both statements: We can plug the values into our formula: $$60 = \frac{300}{(S_f - 80) \times \frac{5}{18}}$$ This gives us one equation with a single unknown variable, $S_f$. Therefore, we can solve for the speed of the faster train. ### Exam Strategy & Shortcut To find one unknown ($S_f$) in the standard crossing formula $T = \frac{D}{Relative Speed}$, you need the other three parts: Time (given in question), Distance (given in II), and the other speed component (given in I). Thus, both are necessary. ### Common Pitfall Trying to calculate the exact final speed is a waste of time. Once you realize the equation resolves to a single unknown, you know the data is sufficient. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question**.