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 m. \[\therefore \] According to question, Speed of the train \[=\frac{x}{10}\text{m/s}\] And also the speed of the train \[=\left( \frac{x+50}{14} \right)\text{m/s}\] Both the speeds should be equal i.e., \[\frac{x}{10}=\frac{x+50}{14}\] \[\Rightarrow \] \[14x=10x+500\] \[\Rightarrow \] \[14x-10x=500\] \[\Rightarrow \] \[4x=500\] \[\therefore \] \[x=125\,\,\text{m}\] \[\therefore \] Speed \[=\frac{125}{10}=12.5\,\,\text{m/s}\] \[=\frac{12.5\times 18}{5}\,\,\text{km/h}=45\,\,\text{km/h}\]
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