| A 125 m long train take 25 s to cross a person who is going in the same direction with the speed of 4 km/h. After crossing that person, the train can reach next station in 30 min. How long that person takes to reach that station after being crossed by them? |
A) \[3\frac{1}{4}h\]
B) \[2\frac{3}{4}h\]
C) \[3\frac{3}{4}h\]
D) \[2\frac{1}{4}h\]
Correct Answer: B
Solution :
| Speed of the person \[=4\,\,km/h\] |
| \[=4\times \frac{5}{18}m/s=\frac{10}{9}m/s\] |
| Let speed of train be \[x\,\,m/s.\] |
| Then, relative speed of train \[=\left( x-\frac{10}{9} \right)m/s\] |
| As, train takes 25 s to cross the person. |
| \[\therefore \] \[25=\frac{125}{\left( x-\frac{10}{9} \right)}\]\[\Rightarrow \]\[x-\frac{10}{9}=5\] |
| \[\Rightarrow \] \[x=\frac{55}{9}m/s\] |
| Now, distance covered by the train in 30 min |
| \[=\frac{55}{9}\times 30\times 60\] |
| \[=11000\,\,m=11\,\,km\] |
| Thus, time taken by the person to cover the distance of |
| \[11\,\,km=\frac{11}{4}h=2\frac{3}{4}h\] |
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