# A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

A. 400 m
B. 450 m
C. 560 m
D. 600 m

A. 400 m

Solution: \begin{array} { l } { \text { Let the length of the first train be } x \text { metres. } } \\
\ { \text { Then, the length of the second train is } ( \frac { x } { 2 } )}\\
{ \text { metres. } } \\
\ { \text { Relative speed } = ( 48 + 42 ) kmph =}\\
{ ( 90 \times \frac { 5 } { 18 } ) m / sec = 25 m / sec } \\
\ { \therefore \frac { [ x + ( x / 2 ) ] } { 25 } = 12 \text { or } \frac { 3 x } { 2 } = 300 \text { or } x = 200 . } \\
\ { \therefore \text { Length of first train } = 200 m \text { . } } \\
\ { \text { Let the length of platform be } y \text { metres. } } \\
\ { \text { Speed of the first train } = ( 48 \times \frac { 5 } { 18 } ) m / sec =}\\
{ \frac { 40 } { 3 } m / sec . } \\
\ { \therefore ( 200 + y ) \times \frac { 3 } { 40 } = 45 } \ { \Rightarrow 600 + 3 y = 1800 } \\
\ { \Rightarrow y = 400 m } \end{array}