Question

A train running at 25km/hr takes 18 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5km/hr in the opposite direction. Find the sum of the length of the train and that of the platform?
A. 125m
B. 135m
C. 145m
D. 155m

Answer 1

Hint: We will use the formula \[distance\text{ }=\text{ }speed~\times time\], also we need to convert distance into metre by multiplying it with 1000 and time into hours by dividing it with 3600. From the distance covered by train in 18 seconds and in the second relation we will find the distance covered by train in 12 seconds, this will give us the length of platform and train.

Complete step-by-step answer:
It is given in the question that a train running at 25km/hr takes 18 seconds to pass the platform. Also, the train takes 12 seconds to pass a man walking at 5km/hr to the opposite direction of the train, then we have to find out the sum of the train and that of the platform.
We know that \[distance\text{ }=\text{ }speed~\times time\], we will first convert km/hr to m/hr. By multiplying 25 with 1000 as 25000m, we get, speed of the train \[=25000m/hr\], also, we will convert time = 18 seconds in hours by dividing it with 3600.
So, now, the speed of the train will be 25000m/hr and time taken to cover the platform is $\dfrac{18}{3600}hrs$.
We know that \[distance\text{ }=\text{ }speed~\times time\], therefore, distance covered by train in $\dfrac{18}{3600}hrs$ with speed of 25000m/hr $=25000\times \dfrac{18}{3600}=125m$.
Now, in the second case, when the speed of the train will be (25 + 5) Km/hr = 30km/hr. This is because the man is moving opposite to the train. Also, distance travelled by train in 12 seconds with speed 30km/hr \[=\text{ }speed~\times time\].
But our speed is given in km/hr, we need to convert it into m/s by multiplying it with $\dfrac{5}{18}$, we get
Speed of train $=30\times \dfrac{5}{18}=\dfrac{25}{3}m/s$, thus distance travelled in 12 seconds = $\dfrac{25}{3}\times 12=100m$.
Also, the speed of the train = 25km/hr. We will convert 25km/hr in m/s by multiplying with $\dfrac{5}{18}$. Therefore, we get,
Speed of train = $25\times \dfrac{5}{18}=\dfrac{125}{18}$.
Therefore, the distance covered in 18 seconds = $\dfrac{125}{18}\times 18=125m$.
Thus, we get the length of the train + length of the platform = 125m. Now, the length of the platform will be $\left( 125-100 \right)m=25m$.
Therefore, length of train = 100m, the length of platform=25m and the length of train and platform = $100+25m=125m$, and option a) is correct.

Note: Students may take the speed of a train at 25km/hr even in the second case when the train is passing opposite to the man, which is wrong. We need to take the spread of the train as $25+5=30km/hr$ because the man moves in an opposite direction with a speed of 5km/hr. If the man will move in the direction of the train with the same speed then the speed of the train will be taken as $25-5=20km/hr$. This concept is called relative velocity.