A Train Traveling at 72kmph Crosses a Platform in 30 seconds GMAT Problem Solving

Question: A train traveling at 72kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

1. 240 meters
2. 360 meters
3. 420 meters
4. 600 meters
5. Cannot be determined

Solution and Explanation:

Approach Solution (1):

In speed-distance questions
Pole, a man (stationary) etc are considered as points, when a train crosses these; it means that the train traveled a distance equal to its own length.
While,
Other trains, railway platforms etc are considered for their own lengths, it means that if a moving train crosses these, the train traveled a distance equal to its own length + length of the other train/platform.
Now looking at the question, we can see that:

Speed of the train: 72 km/h = \(72*\frac{5}{18}=20\) meters/sec

Train crosses a man (a stationary point) in 18 seconds: Train covers it own length in 18 seconds:
Length of train = 20 * 18 = 360 meters

Train crosses a platform in 30 seconds: Train covers a distance equal to its own length + length of the platform in 30 seconds:
i.e. length of train +length of the platform = 20 * 30 (Distance = Speed * Time)
360 + x = 600
x = 240
Length of platform = 240 meters

Correct Option: A

Approach Solution (2):

Let’s use some graphics to help see what’s happening here.
We will say that the train starts crossing the platform when the front nose of the train meets the beginning edge of the platform…

And the train finishes crossing the platform when the back end of the train crosses the end of the platform…

Let p = length of the platform (in meters)
Let t = length of the train (in meters)
We will also add a blue dot at the front of the train to help determine the distance the train travels.
Below, we have the train when it first meets the platform.

Below, we have the train when it finishes crossing the platform

During this period, the total distance the train (and the blue dot) travels = p + t meters

Important: At this point, we better convert all units to meters and seconds
Given: A train traveling at 72 kmph crosses a platform in 30 seconds
1 kilometer = 1000 meters
So, 72 kilometers per hour = 72000 meters per hour
There are 3600 seconds in an hour
So, 72000 meters per hour = 72000 meters per 3600 seconds
= 20 meters per second

So, the train’s speed = 20 meters per second
Distance = (speed) (time)
So, if the train travels for 30 seconds at a speed of 20 meters per second, the distance traveled = (20)(30) = 600 meters
We already know that the train travels = p + t meters

So, we can write: p + t = 600
Now, if the train travels for 18 seconds at a speed of 20 meters per second, the distance traveled = (20)(18) = 360 meters
We already know that the distance the train travels = t meters
So, we can write: t = 360

At this point, we know that:
p + t = 600
t = 360
Subtract the bottom equation from the top equation to get: p = 240

Correct Option: A

Approach Solution (3):

We can let p = the length of the platform, in meters, and t = the length of the train, in meters

When we say the train crosses a platform in 30 seconds, it really means it takes 30 seconds for the nose of the train to enter one end of the platform and the rear of the train to exit the other end of the platform. Thus, in 30 seconds, not only does the train’s nose travel the entire length of the platform but also its entire body length does. Thus, we have (notice that 72 kmph = 72000 meters per hour, and 30 seconds = \(\frac{30}{3600}= \frac{1}{120}hr)\):

\(72000*\frac{1}{120}=p+t\)
\(600=p+t\)
\(p=600-t\)

We are also given that the train crosses a man (whose body width is negligible) standing on the platform in 18 seconds. So when the train crosses him, it only travels its body length in 18 seconds.

\(72000*\frac{1}{120}=t\)
\(t=360\)
Therefore, the platform has a length of 600 – 360 = 240 meters

Correct Option: A

“A train traveling at 72kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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