A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

A. 565
B. 500
C. 450
D. 498

Solution:

\[\left. \begin{array} { l } { \text { Speed } = ( 78 \times \frac { 5 } { 18 } ) m / sec = ( \frac { 65 } { 3 } ) m / sec } \\ { \text { Time } = 1 \text { minute } = 60 \text { seconds. } } \\ { \text { Let the length of the tunnel be } x \text { metres. } } \\ { \text { Then, } ( \frac { 800 + x } { 60 } ) = \frac { 65 } { 3 } } \\ { \Rightarrow 3 ( 800 + x ) = 3900 } \\ { \Rightarrow x = 500 } \end{array} \right.\]

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