Question

It takes 15 seconds for a train travelling at 60 km/hr to cross entirely another train half its length and travelling in the opposite direction at 48 km/hr. It also passes a bridge in 51 seconds. The length of the bridge is:
A) 550 m
B) 450 m
C) 500 m
D) 600 m

Answer 1

Hint: For solving this question we will first find the speed of the train by using the concept that when two moving bodies are moving in the same direction, then the net speed of the motion is taken as the difference of their speeds and when two moving bodies are moving in the opposite direction, then the net speed of the motion is taken as the sum of their speeds. Later, we will find the length of the bridge using the speed, distance and time relation, which is given as follows: \[distance=speed\times time\]

Complete step by step solution:
As mentioned in the question, we have to find the length of the bridge.
Now, let us assume the length of the train is $x$ . So, as mentioned in the question, using the distance formula, we can write as
\[\begin{align}
  & x+\dfrac{x}{2}=\left( 60+48 \right)\times \dfrac{15}{60\times 60} \\
 & \Rightarrow \dfrac{3x}{2}=\dfrac{\left( 48+60 \right)}{240} \\
 & \Rightarrow 360x=108 \\
 & \Rightarrow x=0.3km \\
\end{align}\]
As we know that the value of 1 kilometer is 1000 meters. Hence the value of $0.3km$ will be $300m$ .
Let us assume that the length of the bridge is $l$.
Now, for calculating the length of the bridge, we will take the total distance covered by the train, which is $300+l$ equal to $speed\times time$. Here the speed is 51km/h for converting it into m/s we will multiply it with $\dfrac{5}{18}$.
By performing these steps, we get
\[\begin{align}
  & 300+l=51\times 60\times \dfrac{5}{18} \\
 & \Rightarrow 300+l=850 \\
 & \Rightarrow l=550m \\
\end{align}\]

Hence, the length of the bridge is 550m

Note: While solving this question we should be careful with the direction in which the two trains are moving because from the concept we have that when two moving bodies are moving in the same direction, then the net speed of the motion is taken as the difference of their speeds and when two moving bodies are moving in the opposite direction, then the net speed of the motion is taken as the sum of their speeds. For example if we consider the reverse and solve this question then we will have the result as
\[\begin{align}
  & x-\dfrac{x}{2}=\left( 60-48 \right)\times \dfrac{15}{60\times 60} \\
 & \Rightarrow \dfrac{x}{2}=\dfrac{\left( 12 \right)}{240} \\
 & \Rightarrow x=0.1km \\
\end{align}\]
Now the total distance covered by the train will be
\[\begin{align}
  & 100+l=51\times 60\times \dfrac{5}{18} \\
 & \Rightarrow 100+l=850 \\
 & \Rightarrow l=750m \\
\end{align}\] .
This is not even in the options so it is clearly a wrong answer.