Question
Length of train ‘M’ is ___ metres, which is ____
metres more than that of train ‘N’. Speed of ‘N’ and ‘M’ are ____ m/s and ____ m/s respectively. Time taken by trains to cross each other when moving in the same direction and in opposite direction is 120 seconds and 40 seconds, respectively. The values given in which of the following options will fill the blanks in the same order in which they are given to make the statement true: I. 600, 120, 9, 18 II. 780, 120, 12, 24 III. 700, 100, 10, 20Solution
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.
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