A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x?

$$\eqalign{ & {\text{Let the length of train}} = l{\text{ km}} \cr & \frac{{l + 0.2}}{x} = \frac{{30}}{{3600}} \cr & 120\left( {l + 0.2} \right) = x \cr & 120\left( {l + 24} \right) = x{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & \frac{l}{{x - 6}} = \frac{{20}}{{3600}} \cr & 180l = x - 6 \cr & 180l + 6 = x{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{From equation }}\left( {\text{i}} \right)\,\& \,\left( {{\text{ii}}} \right) \cr & 120l + 24 = 180l + 6 \cr & 60l = 18 \cr & l = \frac{3}{{10}} \cr & {\text{Now from equation }}\left( {\text{i}} \right) \cr & 120 \times \frac{3}{{10}} + 24 = x \cr & x = 60{\text{ km/h}} \cr} $$