| A train travelling at 48 km/h crosses another train, having half its length and travelling in opposite directions at 42 km/h in 12 s. It also passes a railway platform in 46 s. The length of the railway platform is |
A) 200 m
B) 300 m
C) 350 m
D) 400 m
Correct Answer: D
Solution :
| Let the length of the train travelling at \[48km/h\]be \[x\,\,m.\] |
| Let the length of the platform be \[y\,\,m.\] |
| Relative speed of train |
| \[=(48+42)\,\,km/h\] |
| \[=90\times \frac{5}{18}m/s=25m/s\] |
| Now, \[\frac{x+\frac{x}{2}}{25}=12\]\[\Rightarrow \]\[\frac{3x}{50}=12\] |
| \[\Rightarrow \] \[3x=12\times 50\] |
| \[\Rightarrow \] \[x=4\times 50=200\,\,m\] |
| Again, \[\frac{200+y}{45}=48\times \frac{5}{18}\] |
| \[\Rightarrow \]\[\frac{200+y}{45}=\frac{40}{3}\] |
| \[\Rightarrow \]\[600+3y=1800\] |
| \[\Rightarrow \]\[3y=1200\]\[\Rightarrow \]\[y=400\] |
| \[\therefore \]Length of railway platform \[=400\,\,m\] |
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