Question

The length of the bridge, which a train 130 meters long and travelling at \[45{\rm{km/hr}}\] can cross in 30 seconds, is
A.200 m
B.225 m
C.245 m
D.250 m

Answer 1

Hint: Here we need to find the length of the train. We will first assume the length of the bridge to be any variable. Then we will find the distance covered by the train which will be equal to the speed of the train and time taken to cover that distance. However, the distance is also equal to the sum of the length of bridge and train. So we will equate both the distances and solve it further to get the value of the length of the bridge.

Complete step-by-step answer:
Here we need to find the length of the bridge.
Let the length of the bridge be \[x\].
It is given that the length of the train is 130 meters and the train takes 30 seconds when travelling at the speed of \[45{\rm{km/hr}}\].
Now, we will change the unit of the speed of the train from \[{\rm{km/hr}}\] to \[{\rm{m/s}}\].
We know that:
\[1{\rm{km/hr}} = \dfrac{5}{{18}}{\rm{m/s}}\]
Therefore,
 \[45{\rm{km/hr}} = 45 \times \dfrac{5}{{18}}{\rm{m/s}} = \dfrac{{25}}{2}{\rm{m/s}}\]
The distance covered by the train will be equal to the sum of the length of the bridge and the length of the train.
Distance travelled by train \[ = \left( {130 + x} \right)m\] ………………………………………..\[\left( 1 \right)\]
We know the formula to calculate the distance is given by \[{\rm{distance}} = {\rm{speed}} \times {\rm{time}}\].
Now, we will use this formula to calculate the distance covered by the train.
So, substituting \[{\rm{speed}} = \dfrac{{25}}{2}\] and \[{\rm{time}} = 30\] in the formula \[{\rm{distance}} = {\rm{speed}} \times {\rm{time}}\], we get
Distance travelled by train \[ = \dfrac{{25}}{2} \times 30\]
Now as both the distances are the same, we will equate them. Therefore, we get
\[ \Rightarrow 130 + x = \dfrac{{25}}{2} \times 30\]
On multiplying the terms, we get
\[ \Rightarrow 130 + x = 375\]
Now, subtracting 130 from both sides, we get
\[\begin{array}{l} \Rightarrow 130 + x - 130 = 375 - 130\\ \Rightarrow x = 245\end{array}\]
Therefore, the required length of the bridge is equal to \[245m\].
Hence, the correct option is option C.

Note: Here, we might make a mistake by calculating the distance just by using the length of the train and not the length of the bridge, hence this will give us the wrong answer. Here we have to add the length of the bridge to the length of the train and not subtract it as this will give us the wrong answer. Also, the unit of all the dimensions should be the same because if the units are different then we cannot mathematically operate it, even if we try we will get an incorrect answer. That is why we changed the unit of speed from \[{\rm{km/hr}}\] to \[{\rm{m/s}}\].