The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{two}}\,{\text{trains}}\,{\text{be}}\,7x\,{\text{and}}\,8x\,{\text{km/hr}} \cr & {\text{Then}},\,8x = {\frac{{400}}{4}} = 100 \cr & \Rightarrow x = {\frac{{100}}{8}} = 12.5 \cr & \therefore {\text{Speed}}\,{\text{of}}\,{\text{first}}\,{\text{train}} \cr & = \left( {7 \times 12.5} \right){\text{km/hr}} \cr & = 87.5\,{\text{km/hr}} \cr} $$