| A train, 300 m long, passed a man, walking along the line in the same direction at the rate of 3 km/h in 33 s. The speed of the train is [SSC (CGL) 2010] |
A) \[30\,\,km/h\]
B) \[32\frac{8}{11}km/h\]
C) \[32\,\,km/h\]
D) \[35\frac{8}{11}km/h\]
Correct Answer: D
Solution :
| Given, length of train \[=300\,\,m\] |
| Let train's speed be \[x\,m/s.\] |
| \[\text{Time}=33\,\,s\] |
| Man's speed \[=3\,\,km/h=\frac{3\times 5}{18}m/s=\frac{5}{6}m/s\] |
| \[\therefore \]Relative speed = Train's speed \[-\]Man's speed |
| \[=x-\frac{5}{6}\] |
| Then, \[x-\frac{5}{6}=\frac{300}{33}\] |
| \[\Rightarrow \] \[\frac{6x-5}{6}=\frac{300}{33}=\frac{100}{11}\] |
| \[\Rightarrow \] \[x=\frac{655}{66}m/s\] |
| \[=\frac{655}{66}\times \frac{18}{5}=35\frac{8}{11}km/h\] |
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