Speed of two trains 'A' and 'B' is 27 m/s and ___ m/s respectively. Length of 'B' and 'A' is ___ metres and 270 metres, respectively. Time taken by the trains to cross each other when moving in same direction is 54 seconds. The data given in which among the given options will fill the blank in the same order so as to make the statement true?
I. 34, 108
II. 25, 300
III. 18, 216

Solution

Statement I: Relative speed = 34 - 27 = 7 m/s
Sum of length of both the trains = 108 + 270 = 378 metres
Time taken to cross each other = (378/7) = 54 seconds So, statement I is true. Statement II: Relative speed = 27 - 25 = 2 m/s
Sum of length of both the trains = 300 + 270 = 570 metres
Time taken to cross each other = (570/2) = 285 seconds So, statement II is false. Statement III: Relative speed = 27 - 18 = 9 m/s
Sum of length of both the trains = 216 + 270 = 486 metres
Time taken to cross each other = (486/9) = 54 seconds So, statement III is true. Therefore, both statement I and III are true. Hence, option B.