A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{second}}\,{\text{train}}\,{\text{be}}\,x\,{\text{km/hr}}. \cr & {\text{Relative}}\,{\text{speed}}\, \cr & = \,\left( {x + 50} \right)\,{\text{km/hr}} \cr & = \left[ {\left( {x + 50} \right) \times \frac{5}{{18}}} \right]\,{\text{m/sec}} \cr & = {\frac{{250 + 5x}}{{18}}} \,{\text{m/sec}} \cr & {\text{Distance}}\,{\text{covered}} \cr & = \left( {108 + 112} \right) = 220\,m \cr & \therefore \frac{{220}}{{ {\frac{{250 + 5x}}{{18}}} }} = 6 \cr & \Rightarrow 250 + 5x = 660 \cr & \Rightarrow x = 82\,{\text{km/hr}} \cr} $$