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.50 m
B.60 m
C.69 m
D.70 m

Solution:

\begin{array} { l } { 2 kmph = ( 2 \times \frac { 5 } { 18 } ) m / sec = \frac { 5 } { 9 } m / sec } \\
\ { 4 kmph = ( 4 \times \frac { 5 } { 18 } ) m / sec = \frac { 10 } { 9 } m / sec } \\
\ { \text { Let the length of the train be } x metres}\\
{\text { and its speed by } y m / sec \text { . } } \\
\ { \text { Then, } ( \frac { x } { y – \frac { 5 } { 9 } } ) = 9 \text { and } ( \frac { x } { y – \frac { 10 } { 9 } } ) = 10 . } \\
\ { \therefore 9 y – 5 = x \text { and } 10 ( 9 y – 10 ) = 9 x } \\
\ { \Rightarrow 9 y – x = 5 \text { and } 90 y – 9 x = 100 . } \\
\ { \text { On solving, we get: } x = 50 . } \\
\ { \therefore \text { Length of the train is } 50 m \text { . } } \end{array}

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