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      Question

      The question consists of two statements numbered “I

      and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. What is the length of Rajdhani Express? Statement-I: Rajdhani Express can cross a platform of length three times of its length in 32 sec, while it can cross a pole in 8 sec. Statement-II: Rajdhani Express can cross Shatabdi Express in 15 sec and 45 sec while moving in opposite direction and in same direction respectively, it is given that speed of Shatabdi Express is 25 m/s.
      A 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. Correct Answer Incorrect Answer
      B 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. Correct Answer Incorrect Answer
      C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
      D The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
      E The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

      Solution

      Let, length and speed of Rajdhani express be ‘l’ m and ‘v’ m/s respectively. Statement-I: So, length of platform = 3l So, (l + 3l)/v = 32 ------(i) Also, l/v = 8 ------(ii) As both equations are same, question can’t be solved by using statement-I alone. So, data in statement I alone is not sufficient to answer the question. Statement-II: Let, length and speed of Rajdhani express be ‘l’ m and ‘v’ m/s respectively. Let the length of Shatabdi express be ‘x’ m. So, according to question: l + x = 15 × (25 + v) ---------(i) Also, l + x = 45 × (v – 25) --------------(ii) Solving (i) and (ii), we get v = 50 So, the speed of Rajdhani express = 50 m/s Length of Rajdhani express can’t be determined. So, data in statement II alone is not sufficient to answer the question. Combining statement I and statement II: Length of Rajdhani express = 50 × 8 = 400 m So, data in statement I and statement II together are necessary to answer the question.

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