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A train 100 meters long running at 54km/hr takes 20 seconds to pass a bridge. The length of the bridge is:
a. 50 meter
b. 150 meter
c. 200 meter
d. 620 meter

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Last updated date: 20th Jun 2024
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Answer
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Hint: We will take the length of the bridge as ‘x’ and the length of the train as ‘y’. So, the total distance covered by the train will become ‘x + y’. We have been given the values of speed of the train and the time taken by the train, so by substituting these values in the below formula we will get the answer,
\[Time\ \ =\ \ \dfrac{Dis\tan ce}{Speed}\]
We will also convert the speed from km/hr to m/s, by multiplying it with 5 and then dividing the product with 18.

Complete step-by-step answer:
For solving this question, we will be following the steps which are given below.
We will take the length of the bridge to be ‘x’ and the length of the train to be ‘y’.
So, the distance covered by the train is equal to ‘y + x’. Time taken by the train to cover this distance is 20 seconds. The speed of the train is 54km/hr.
So, we will now form an equation and put the values in this to obtain the answer. The following is the equation:-
\[Time\ \ =\ \ \dfrac{Dis\tan ce}{Speed}\]
Speed of the train = 54km/hr
= \[54\ \ \times \ \ \dfrac{5}{18}\]
= \[3\ \ \times \ \ 5\ \]
= 15m/s
Distance covered by the train = \[x\ \ +\ \ y\]
= \[x\ \ +\ \ 100\]
Time taken by the train to cover this distance = 20 seconds
Length of the bridge = \[Time\ \ =\ \ \dfrac{Dis\tan ce}{Speed}\]
\[\begin{align}
  & \Rightarrow \dfrac{x\ \ +\ \ 100}{15}\ \ =\ \ 20 \\
 & \Rightarrow x\ \ +\ \ 100\ \ =\ \ 20\ \ \times \ \ 15 \\
 & \Rightarrow x\ \ +\ \ 100\ \ =\ \ 300 \\
 & \Rightarrow x\ \ =\ \ 300\ \ -\ \ 100 \\
 & \Rightarrow x\ \ =\ \ 200 \\
\end{align}\]
So, as per the above calculation, the length of the bridge is 200 meters.
So, the correct answer is “Option C”.

Note: Let us now know about some other formulas too.
\[\Rightarrow Dis\tan ce\ \ =\ \ Time\ \ \times \ \ Speed\]
\[\begin{align}
  & \Rightarrow Speed\ \ =\ \ \dfrac{Dis\tan ce}{Time} \\
 & \\
\end{align}\]
These are the formulas to find Time when Distance and Speed is given, or to find Distance when Time and Speed are given. Also, when we have to convert m/s to km/hr, we first multiply the speed with 18 and then divide that product by 5.