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. Find the length of train ?

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A. 45 meter

B. 50 meter

C. 55 meter

D. 60 meter

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Correct Answer : B.

First person speed = 2*(5/18) = 5/9 m/sec
Second person speed = 4*(5/18) = 10/9 m/sec
Let the length of train is x metre and speed is y m/sec
then,

\frac{x}{y - \frac{5}{9}} = 9 \Rightarrow 9 y - 5 = x \Rightarrow 9 y - x = 5 . . . (i) A l s o, \frac{x}{y - \frac{10}{9}} = 10 90 y - 9 x = 100 . . . (i i) f o r m (i) a n d (i i), w e g e t, x = 50

So length of train is 50 metre