A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph respectively and passes them completely in 9 and 10 seconds respectively. The length of the train is ______ metres.
Solution
Correct Answer: Option C
Let the speed of the train be ‘x’ kmph and it’s length be ‘y’ km
Case 1: Relative to person 1
∵ the train and 1st person are travelling in the same direction,
Relative speed = (x – 2) kmph
Distance travelled by train in crossing the person = y km
Time taken = 9 seconds = 9/3600 hrs
But we know that,
Distance = speed × Time
∴ y = (x – 2) × (9/3600) -----(1)
Case 2: Relative to person 2
∵ the train and 2nd person are travelling in the same direction,
Relative speed = (x – 4) kmph
Distance travelled by train in crossing the person = y km
Time taken = 10 seconds = 10/3600 hrs
But we know that,
Distance = speed × Time
∴ y = (x – 4) × (10/3600) -----(2)
∴ on equating equations (1) and (2) we get,
\(\left( {{\rm{x}} - 4} \right){\rm{\;}} \times {\rm{\;}}\frac{{10}}{{3600}}{\rm{\;}} = {\rm{\;}}\left( {{\rm{x\;}}-{\rm{\;}}2} \right){\rm{\;}} \times {\rm{\;}}\frac{9}{{3600}}\)
∴ x = 22 kmph
Substituting the value of x in equation (1) we get,
Y = 50 meters
Thus the length of the train is 50 meters
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