| A train 160 m long takes 8 s to cross a man running at 8 km/h in the direction opposite to that of the train. Find the speed of the train. |
A) 64 km/h
B) 65 km/h
C) 61 km/h
D) 68 km/h
Correct Answer: A
Solution :
| Let the speed of the train be x km/h. |
| Relative speed \[=(x+8)km/h\] |
| \[=\frac{5\,(x+8)}{18}m/s\] |
| Relative speed |
| \[=\frac{\text{Length}\,\,\text{of}\,\,\text{the}\,\,\text{train}}{\text{Time}\,\,\text{taken}\,\,\text{by}\,\,\text{train}\,\,\text{to}\,\,\text{pass}\,\,\text{the}\,\,\text{man}}\] |
| \[\Rightarrow \]\[\frac{5\,\,(x+8)}{18}=\frac{160}{8}\] |
| \[\Rightarrow \]\[x+8=\frac{160\times 18}{5\times 8}=72\] |
| \[\Rightarrow \]\[x=72-8=64\,\,km/h\] |
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