Question

A 300 m long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
A. 250 m
B. 300 m
C. 350 m
D. 120 m

Answer 1

Hint: We will first find the speed of the train using the given data about the length of the train and the time in which the train crosses the pole. After this, we can use the same data to find the length of the platform by assuming it to be ‘x’.

Complete step-by-step solution:
Let us assume that the length of the platform is ‘x’ meters.
We know that the formula of distance is given by speed multiplied by the time. This can be represented as follows:
$ \Rightarrow $ Distance = $Speed \times Time$
Rearranging the terms to get the following expression:-
$ \Rightarrow Speed = \dfrac{{Dis\tan ce}}{{Time}}$ ……………..(1)
Using the given data that train is 300 m long and it crosses the pole in 18 seconds in the above expression, we will then obtain the following:-
$ \Rightarrow Speed = \dfrac{{300}}{{18}}$ m / sec.
Simplifying the RHS by dividing both the numerator and denominator by 6, we will then obtain:-
$ \Rightarrow Speed = \dfrac{{50}}{3}$ m / sec. ……………….(2)
Now, we have the speed of train with us.
Now, when the train crosses the platform, it has to cover two distances that is the train’s and the platform.
So, the total distance the train needs to cover is ‘x + 300’ meters.
Now, putting this distance above and the fact that it crosses the platform in 39 seconds, we will get:-
$ \Rightarrow Speed = \dfrac{{x + 300}}{{39}}$ m / sec.
Since, the speed of train will remain constant, therefore, let us put the equation (2) in the above expression so that we will obtain the following expression:-
$ \Rightarrow \dfrac{{50}}{3}m/\sec = \dfrac{{x + 300}}{{39}}m/\sec $
Since the units are same on both sides, we can cross them off to get:-
$ \Rightarrow \dfrac{{50}}{3} = \dfrac{{x + 300}}{{39}}$
Cross – multiplying the both sides to get the following expression:-
$ \Rightarrow 50 \times 39 = 3\left( {x + 300} \right)$
Simplifying the calculations on both the sides, we will then obtain:-
$ \Rightarrow 1950 = 3x + 900$
Re – arranging the terms to get the following expression:-
$ \Rightarrow 3x = 1950 - 900$
Simplifying the RHS to get:-
$ \Rightarrow 3x = 1050$
$ \Rightarrow x = \dfrac{{1050}}{3} = 350$
Hence, the length of the platform is 350 meters.

$\therefore $ The correct option is (C).

Note: The students must note that pole is like a point to cross because pole does not have length but only height, so when the train crosses it, it must cover the whole length of train only and thus we used the distance as the length of train in the formula and while crossing the platform, the whole train had to cover both the length of platform and the length of train as well.
The students must commit to memory the following formula:-
$ \Rightarrow $ Distance = $Speed \times Time$