Length of train ‘M’ is ___ metres, which is ____

Solution

Statement I: Length of 'M' = 600 metres Length of 'N' = 600 − 120 = 480 metres Speed of 'N' = 9 m/s Speed of 'M' = 18 m/s Time taken by them to cross each other when moving in same direction: = (600 + 480) ÷ (18 − 9) = (1080/9) = 120 seconds Time taken by them to cross each other when moving in opposite direction: = (600 + 480) ÷ (18 + 9) = (1080/27) = 40 seconds So, statement I is true. Statement II: Length of 'M' = 780 metres Length of 'N' = 780 − 120 = 660 metres Speed of 'N' = 12 m/s Speed of 'M' = 24 m/s Time taken by them to cross each other when moving in same direction: = (780 + 660) ÷ (24 − 12) = (1440/12) = 120 seconds Time taken by them to cross each other when moving in opposite direction: = (780 + 660) ÷ (24 + 12) = (1440/36) = 40 seconds So, statement II is true. Statement III: Length of 'M' = 700 metres Length of 'N' = 700 − 100 = 600 metres Speed of 'N' = 10 m/s Speed of 'M' = 20 m/s Time taken by them to cross each other when moving in same direction: = (700 + 600) ÷ (20 − 10) = (1300/10) = 130 seconds Time taken by them to cross each other when moving in opposite direction: = (700 + 600) ÷ (20 + 10) = (1300/30) = 43.33 seconds So, statement III is false. Therefore, both statement I and II are true. Hence, option D.