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1. Train A passes a lamp post in 9 seconds and 700 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long? (in seconds)

A. 32 seconds

B. 31 seconds

C. 33 seconds

D. 30 seconds

Solution:

\begin{aligned} Let the length of train be x m \\ When a train crosses a light \\ post in 9 second the distance covered \\ =  length of train \\ \Rightarrow speed of train  = \frac{x}{9} \\ Distance covered in crossing a \\ 700 meter platfrom in 30 seconds \\ =  Length of platfrom  +  length of train \\ Speed of train  = \frac{x + 700}{30} \\ \Rightarrow \frac{x}{9} = \frac{x + 700}{30} [∵ Speed  = \frac{Distance}{Time}] \\ \Rightarrow \frac{x}{3} = \frac{x + 700}{10} \\ \Rightarrow 10 x = 3 x + 2100 \\ \Rightarrow 10 x - 3 x = 2100 \\ \Rightarrow 7 x = 2100 \\ \Rightarrow x = \frac{2100}{7} = 300 m \\ When the length of the platform be 800m, \\ then time T be taken by train to cross 800m \\ long platform \\ \frac{x}{9} = \frac{x + 800}{T} \\ \Rightarrow T x = 9 x + 7200 \\ \Rightarrow 300 T = 2700 + 7200 \\ \Rightarrow 300 T = 9900 \\ \Rightarrow T = \frac{9900}{300} = 33 seconds \end{aligned}

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