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1. A train passes two bridges of length 500 m and 250 m in 100 seconds and 60 seconds respectively. The length of the train is?

A. 152 m

B. 125 m

C. 250 m

D. 120 m

Solution:

\begin{aligned} Let the length of train x m \\ Speed of train \\ = \frac{(Length of train  +  length of bridge)}{Time taken in crossing} \\ According to information we get \\ \Rightarrow \frac{x + 500}{100} = \frac{x + 250}{60} \\ \Rightarrow 60 (x + 500) = 100 (x + 250) \\ \Rightarrow 3 (x + 500) = 5 (x + 250) \\ \Rightarrow 5 x + 1250 = 3 x + 1500 \\ \Rightarrow 5 x - 3 x = 1500 - 1250 \\ \Rightarrow 2 x = 250 \\ \Rightarrow x = \frac{250}{2} = 125 m \end{aligned}

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