Question

A good train runs at a speed of $72$ km/hr and crosses $250$ m long platform in $26$ seconds. What is the length of the good train?
A. $130$m
B. $200$m
C. $270$m
D. $170$m

Answer 1

Hint: Convert all terms in the same unit and then find the total distance covered in crossing the platform after that use the formula given below to get the desired result.
${\text{Time}} = \dfrac{{{\text{Distance}}}}{{{\text{Speed}}}}$

Complete step by step solution:
It is given that the train runs at a speed of $72$ km/hr and crosses $250$ m long platform in $26$ seconds.
We have to find the length of the train using the given data.
We have given the speed of the train in millimeters per hour, first we need to convert it in meters per second. So, multiply the given speed with $\left( {\dfrac{{1000}}{{3600}} = \dfrac{5}{{18}}} \right)$.

So, the speed in meter per second is given as:
Speed$ = \left( {72 \times \dfrac{5}{{18}}} \right)$meters per second
Speed$ = 20$meters per second
So, the speed of the train is $20$ meters per second.

Now, assume that the length of the train be $l$meters. Then we know that a train is said to be crossed through the platform, when the entire train crosses the platform, so the total covered distance to cross the platform contains the length of the train along with the length of the platform. Then the total distance covered in crossing the platform is given as:

Distance covered${\text{ = Length of Platform}} + {\text{length of train}}$
Substitute the values of the platform length and the length of the train.
Distance covered${\text{ = }}\left( {{\text{250}} + l} \right)$

So, the time taken in crossing the platform is given as:
Time taken$ = \dfrac{{{\text{Distance covered}}}}{{{\text{Speed of train}}}}$
Substitute the values:
Time taken$ = \dfrac{{250 + l}}{{20}}$
It is given that the time taken in crossing the platform is $26$ second, so we have
$26 = \dfrac{{250 + l}}{{20}}$
Solve the equation for the value of$l$.
$ \Rightarrow 26 \times 20 = 250 + l$
$ \Rightarrow 520 = 250 + l$
$ \Rightarrow l = 520 - 250$
$ \Rightarrow l = 270$

Therefore, the length of the train is $270$ meters.

Thus, the option (C) is correct.

Note: The total distance covered in crossing the train contains the length of the train because when the initial part of the train crosses the platform, then it can’t be said that the train passed through the platform, so when the entire train crosses the platform then we say that the train crosses the platform.