A. 66 km/hr
B. 72 km/hr
C. 78 km/hr
D. 81 km/hr
D. 81 km/hr
Solution: \begin{array} { l } { 4.5 km / hr = ( 4.5 \times \frac { 5 } { 18 } ) m / sec = \frac { 5 } { 4 } m / sec}\\
{ = 1.25 m / sec , \text { and } } \\
\ { 5.4 km / hr = ( 5.4 \times \frac { 5 } { 18 } ) m / sec = \frac { 3 } { 2 } m / sec }\\
{= 1.5 m / sec } \\
\ { \text { Let the speed of the train be } x m / sec \text { . } } \\
\ { \text { Then, } ( x - 1.25 ) \times 8.4 = ( x - 1.5 ) \times 8.5 } \\
\ { \Rightarrow 8.4 x - 10.5 = 8.5 x - 12.75 } \\
\ { \Rightarrow 0.1 x = 2.25 } \\
\ { \Rightarrow x = 22.5 } \\
\ { \therefore \text { Speed of the train } = ( 22.5 \times \frac { 18 } { 5 } ) km / hr }\\
{= 81 km / hr } \end{array}
Solution: \begin{array} { l } { 4.5 km / hr = ( 4.5 \times \frac { 5 } { 18 } ) m / sec = \frac { 5 } { 4 } m / sec}\\
{ = 1.25 m / sec , \text { and } } \\
\ { 5.4 km / hr = ( 5.4 \times \frac { 5 } { 18 } ) m / sec = \frac { 3 } { 2 } m / sec }\\
{= 1.5 m / sec } \\
\ { \text { Let the speed of the train be } x m / sec \text { . } } \\
\ { \text { Then, } ( x - 1.25 ) \times 8.4 = ( x - 1.5 ) \times 8.5 } \\
\ { \Rightarrow 8.4 x - 10.5 = 8.5 x - 12.75 } \\
\ { \Rightarrow 0.1 x = 2.25 } \\
\ { \Rightarrow x = 22.5 } \\
\ { \therefore \text { Speed of the train } = ( 22.5 \times \frac { 18 } { 5 } ) km / hr }\\
{= 81 km / hr } \end{array}