Question

A train passes over a $400m$ long bridge. If the speed of the train is $30m/s$ and the train takes $20s$ to cross the bridge, find the length of the train.

• A. $400m$
• B. $600m$
• C. $800m$
• D. $200m$

Answer 1

The correct option is D

$200m$

Explanation of the correct option:

(D) 200 m

Step 1: Given

Speed of the train $=30m/s$

Time is taken by train to cross the bridge $=20s$

Length of the bridge = $400m$

Step 2: Calculating length of train

Let the length of the train be $L_T$

Total distance covered by the train = Length of the bridge + length of the train

$$\begin{gathered} \mathrm{Total}\mathrm{distance}=400+{\mathrm{L}}_{\mathrm{T}}---\left(1\right) \\ \mathrm{Total}\mathrm{distance}=\mathrm{Speed}\times \mathrm{Time}---\left(2\right) \\ \mathrm{equation}\left(1\right)\mathrm{and}\left(2\right) \\ 400+{\mathrm{L}}_{\mathrm{T}}=\mathrm{Speed}\times \mathrm{Time} \\ 400+{\mathrm{L}}_{\mathrm{T}}=30\times 20 \\ {\mathrm{L}}_{\mathrm{T}}=600-400=200\mathrm{metres}\left(\mathrm{m}\right) \end{gathered}$$

Thus, the length of the train is $200m$.

Hence, option D is correct.