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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

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Correct Answer :

B. 50 m

2 k m p h = (2 x \frac{5}{18}) m / s e c = \frac{5}{9} m / s e c . 4 k m p h = (4 x \frac{5}{18}) m / s e c = \frac{10}{9} m / s e c . L e t t h e l e n g t h o f t h e t r a i n b e x m e t r e s a n d i t s s p e e d b y y m / s e c . T h e n, (\frac{x}{y - \frac{5}{9}}) = 9 a n d (\frac{x}{y - \frac{10}{9}}) = 10 . T h e r e f o r e 9 y - 5 = x a n d 10 (9 y - 10) = 9 x \Rightarrow 9 y - x = 5 a n d 90 y - 9 x = 100 . O n s o l v i n g, w e g e t : x = 50 . T h e r e f o r e L e n g t h o f t h e t r a i n i s 50 m .

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