A) 24 km/h
B) 26 km/h
C) 40 km/h
D) 45 km/h
E) Other than those given as options
Correct Answer: D
Solution :
Let the length of the train be L and that of platform be P. Then, \[\frac{L+P}{14}=\]Speed of the train ... (i) Again, \[\frac{L}{10}=\]Speed of the train ... (ii) So,\[\frac{L+P}{14}=\frac{L}{10}\] or,\[10L+10P=14L\] or,\[10\times 50=4L\] \[\therefore \]\[L=125\] Therefore speed of the train \[=\frac{125}{10}\times \frac{18}{5}=45\,\,km/h\] Quicker Approach: The train takes 14 - 10 = 4 sec extra to cover the length of platform (50m) \[\therefore \]Speed of train\[=\frac{50}{4}m/s=\frac{50}{4}\times \frac{18}{5}\] = 45 km/hr
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