A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100m and 200m respectively, what is the speed (in kmph) of the train C?

Explanation:-

$$\eqalign{ & {\text{Relative speed of the trains }} \cr & {\text{ = }}\left( {\frac{{100 + 200}}{{2 \times 60}}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {\frac{5}{2}} \right){\text{m/sec}} \cr & {\text{Speed of train B}} \cr & {\text{ = 120 kmph}} \cr & = \left( {120 \times \frac{5}{{18}}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {\frac{{100}}{3}} \right){\text{m/sec}} \cr & {\text{Let the speed of second train be }}x{\text{ m/sec}} \cr & {\text{Then, }}x - \frac{{100}}{3} = \frac{5}{2} \cr & \Rightarrow x = \left( {\frac{5}{2} + \frac{{100}}{3}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{215}}{6}} \right){\text{m/sec}} \cr & \therefore {\text{Speed of second train}} \cr & {\text{ = }}\left( {\frac{{215}}{6} \times \frac{{18}}{5}} \right){\text{ kmph}} \cr & {\text{ = 129 kmph}} \cr}$$