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