A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{length}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{be}}\,x\,{\text{metres}} \cr & \,{\text{and}}\,{\text{its}}\,{\text{speed}}\,{\text{by}}\,y\,{\text{m/sec}} \cr & Then,\,\frac{x}{y} = 15\,\,\,\,\,\, \Rightarrow \,\,\,\,\,y = \frac{x}{{15}} \cr & \therefore \frac{{x + 100}}{{25}} = \frac{x}{{15}} \cr & \Rightarrow 15\left( {x + 100} \right) = 25x \cr & \Rightarrow 15x + 1500 = 25x \cr & \Rightarrow 1500 = 10x \cr & \Rightarrow x = 150m \cr} $$