| A train travelling at 48 km/h completely crosses an another train having half-length of first train and travelling in opposite directions at 42 km/h in 12 s. It also passes a railway platform in 45 s. The length of the platform is |
A) 400 m
B) 450 m
C) 560 m
D) 600 m
Correct Answer: A
Solution :
| Let the length of the first train be am. |
| Then, the length of second train is \[\left( \frac{x}{2} \right)m.\] |
| \[\therefore \]Relative speed \[=(48+42)\,\,km/h\] |
| \[=\left( 90\times \frac{5}{18} \right)=25\,m/s\] |
| According to the question, |
| \[\frac{\left( x+\frac{x}{2} \right)}{25}=12\]\[\Rightarrow \]\[\frac{3x}{2}=300\] |
| \[\Rightarrow \] \[x=200\,\,m\] |
| \[\therefore \]Length of first train \[=200\,\,m\] |
| Let the length of platform be y m. |
| Speed of the first train \[=\left( 48\times \frac{5}{18} \right)m/s=\frac{40}{3}m/s\] |
| \[\text{Time}=\frac{\text{Distance}}{\text{Speed}}\] |
| \[\therefore \]\[(200+y)\times \frac{3}{40}=45\]\[\Rightarrow \]\[600+3y=1800\] |
| \[\therefore \] \[y=400\,\,m\] |
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