A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Correct Answer 50 km/hr

$$\eqalign{ & {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{relative}}\,{\text{to}}\,{\text{man}} \cr & = {\frac{{125}}{{10}}} {\text{ m/sec}} \cr & = {\frac{{25}}{2}} {\text{ m/sec}} \cr & = {\frac{{25}}{2} \times \frac{{18}}{5}} {\text{ km/hr}} \cr & = 45\,{\text{km/hr}} \cr & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{be}}\,x\,{\text{km/hr}}. \cr & \text{Then, relative speed} = \left( {x - 5} \right)\,{\text{km/hr}} \cr & \therefore x - 5 = 45 \cr & \Rightarrow x = 50\,{\text{km/hr}} \cr} $$