Aptitude:: Problems on Trains

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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 and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A. 45 m B. 50 m
C. 54 m D. 72 m

Answer: Option B

Explanation:

 

2 kmph = ( 2 x 5 ( m/sec = 5 m/sec.
18 9

 

4 kmph = ( 4 x 5 ( m/sec = 10 m/sec.
18 9

Let the length of the train be x metres and its speed by y m/sec.

Then, ( x ( = 9 and ( x ( = 10.
y - 5
9
y - 10
9

Therefore 9y - 5 = x and 10(9y - 10) = 9x

=> 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

Therefore Length of the train is 50 m.


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