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?

1152 m
2125 m
3250 m
4120 m

Answer:- 1

Explanation:-

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}

$\eqalign{ & {\text{Let the length of train }}x{\text{ m }} \cr & {\text{Speed of train }} \cr & {\text{ = }}\frac{{\left( {{\text{Length of train + length of bridge }}} \right)}}{{{\text{Time taken in crossing}}}}{\text{ }} \cr & {\text{According to information we get}} \cr & \Rightarrow \frac{{x + 500}}{{100}} = \frac{{x + 250}}{{60}} \cr & \Rightarrow 60\left( {x + 500} \right) = 100\left( {x + 250} \right) \cr & \Rightarrow 3\left( {x + 500} \right) = 5\left( {x + 250} \right) \cr & \Rightarrow 5x + 1250 = 3x + 1500 \cr & \Rightarrow 5x - 3x = 1500 - 1250 \cr & \Rightarrow 2x = 250 \cr & \Rightarrow x = \frac{{250}}{2} = 125\,{\text{m}} \cr}$