A) 24 km/h
B) 36 km/h
C) 40 km/h
D) 45 km/h
Correct Answer: D
Solution :
Let the length of train = x metres \[\therefore \] According to Question, Speed of the train\[=\frac{x}{10}\text{m/s}\] ? (i) And also the speed of the train \[=\left( \frac{x+50}{14} \right)\text{m/s}\] ? (ii) Both the speeds should be equal i.e., \[\frac{x}{10}=\frac{x+50}{14}\] Or \[14x=10x+500\] Or \[14x-10x=500\] Or \[4x=500\] \[\Rightarrow \] \[x=125\,m\] Speed of train \[=\frac{125}{10}\text{m/s}\] [from Eq. (i)] \[=\frac{125}{10}\times \frac{18}{5}=\frac{25}{10}\times 18\] \[=45.0\,\text{km/h}\]
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