Question

A train travelling at 72 kmph 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?

Answer 1

Hint:Here, we can use formula, length of platform = Speed of train $ \times $ extra time taken to cross the platform due to length of platform. We are given the speed of the train and time taken to cross platform and time taken to cross a man. In these types of questions, a man is considered as a point and has no length. So, crossing a man means crossing a point. Change units as speed is given in kmph and time is given in seconds.

Complete step by step answer:
Given that the speed of platform = 72 kmph and it crosses a platform in 30 seconds and it crosses a man in 18 seconds.Here, we can use formula,
Length of the platform = Speed of train $ \times $ extra time taken to cross the platform due to length of platform
Length of the platform = $72\,kmph \times 12\, seconds$
[We cannot directly multiply these numbers as their units are different, first we have to convert kmph to m/s]
Now, units are different
So, we will convert 72 kmph into m/sec
As we know,
1 kmph = $\dfrac{5}{{18}}$ m/s
Therefore, 72 kmph = $\dfrac{5}{{18}} \times 72$ = 20 m/s

Therefore, length of the platform = 20 m/s $ \times $ 12 s = 240 meters.

Note: In these types of questions, we use the concept of speed, time and distance.
Alternatively, we can find the length of the train using its speed and time taken to cross a man.Now, assume length of platform as x, now total distance = length of train + length of platform, taken 30 seconds and speed = 72 kmph. Using formula, find the value of x.