A train travelling at the speed of x km/h crossed a 300 m long platform in 30 second, and overtook a man walking in the same direction at 6 km/h in 20 seconds. What is the value of x?

$$\eqalign{ & {\text{Train speed}} = x{\text{ km/h}} \cr & {\text{Length of train}} = L \cr & {\text{Length of platform}} = 300\,{\text{m}} \cr & {\text{Man's speed}} = 6{\text{ km/h}} \cr & \left( {x - 6} \right) \times \frac{5}{{18}} = \frac{L}{{20}} \cr & 100x - 600 = 18L{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & x \times \frac{5}{{18}} = \frac{{L + 300}}{{30}} \cr & 150x = 18L + 5400 \cr & 150x - 5400 = 18L{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{Equation }}\left( {\text{i}} \right)\,\& \,\left( {{\text{ii}}} \right) \cr & 100x - 600 = 150x - 5400 \cr & 50x = 4800 \cr & x = 96{\text{ km/ h}} \cr} $$