A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in meters?

$$\eqalign{ & {\text{Let the length of the train be x metres}}{\text{.}} \cr & {\text{Then, length of the platform = (2}}x{\text{) metres}}{\text{.}} \cr & {\text{Speed of the train}} \cr & {\text{ = }}\left( {90 \times \frac{5}{{18}}} \right)m/\sec \cr & = 25m/sec \cr & \therefore \frac{{x + 2x}}{{25}} = 36 \cr & \Rightarrow 3x = 900 \cr & \Rightarrow x = 300 \cr & {\text{Hence, length of platform}} \cr & {\text{ = }}2x = \left( {2 \times 300} \right){\text{m}} = 600{\text{m}} \cr} $$