Train A passes a lamp post in 3 seconds and 900 meter long platform in 30 seconds. How much time will same train take to cross a platform which is 800 meters long? (in seconds)

$$\eqalign{ & {\text{Let the length of train be x m}} \cr & {\text{When a train crosses a light }} \cr & {\text{post in 3 second the distance covered}} \cr & {\text{ = length of train }} \cr & \Rightarrow {\text{speed of train = }}\frac{x}{3} \cr & {\text{Distance covered in crossing a}} \cr & {\text{900 meter platfrom in 30 seconds}} \cr & {\text{ = Length of platfrom + length of train}} \cr & {\text{Speed of train = }}\frac{{x + 900}}{30} \cr & \Rightarrow \frac{x}{3} = \frac{{x + 900}}{{30}}\left[ {\because {\text{Speed = }}\frac{{{\text{Distance}}}}{{{\text{Time}}}}} \right] \cr & \Rightarrow \frac{x}{1} = \frac{{x + 900}}{{10}} \cr & \Rightarrow 10x = x + 900 \cr & \Rightarrow 10x - x = 900 \cr & \Rightarrow 9x = 900 \cr & \Rightarrow x = \frac{{900}}{9} = 100{\text{m}} \cr & {\text{When the length of the platform be 800m,}} \cr & {\text{then time T be taken by train to cross 800m}} \cr & {\text{long platfrom}} \cr & \frac{x}{3} = \frac{{x + 800}}{T} \cr & \Rightarrow Tx = 3x + 2400 \cr & \Rightarrow 100T = 300 + 2400 \cr & \Rightarrow 100T = 2700 \cr & \Rightarrow T = \frac{{2700}}{{100}} = 27{\text{ seconds}} \cr} $$