Question

A train takes $18$ seconds to pass through a platform of $162m$ , $15$ seconds to pass through another platform of $120m$ long. The length of the train (in meters) is
A. $70$
B. $80$
C. $\text{90}$
D. $105$

Answer 1

Hint: We need to find the length of the train. Let us assume the length of the train to be $l$ meters. For the length of the platform $=162m$ , the length of the train can be written as $(162+l)m$. Similarly, the length of the train crossing the $120m$ long platform can be written as $(120+l)m$. The main formula that we use is $\text{Speed}=\text{ }\dfrac{\text{Distance}}{\text{Time}}$. We will substitute the values for each case in this equation. Assuming the speed of the train to be constant, let us equate these two equations, that is, \[\text{ }\dfrac{162+l}{18}=\dfrac{120+l}{15}\] . Solving this gives the value of $l$ .

Complete step by step answer:
We need to find the length of the train.
Let us assume the length of the train to be $l$ meters.
It is given that the length of the platform $=162m$ .
Hence, the length of the train can be written as $(162+l)m$ .
We know that $\text{Speed}=\text{ }\dfrac{\text{Distance}}{\text{Time}}$
It is given that the train crosses a $162m$ long platform in $18$ seconds .
Let us write the above equation as
$\Rightarrow \text{Speed}=\text{ }\dfrac{162+l}{18}...(i)$
It is also given that the train crosses a $120m$ long platform in $15$ seconds.
From, this we get the length of the train as $(120+l)m$ and the speed can be written as
$\Rightarrow \text{Speed}=\text{ }\dfrac{120+l}{15}...(ii)$
The speed of the train is constant. Hence, we can equate the equations $(i)$ and $(ii)$ .
Hence, we get
\[\Rightarrow \text{ }\dfrac{162+l}{18}=\dfrac{120+l}{15}\]
Let us solve the equation to get the value of $l$ .
$\Rightarrow 15(162+l)=\text{ 18}(120+l)$
By doing multiplication operation. We will get
$\Rightarrow 2430+15l=\text{ }2160+18l$
Now, let us collect constants to one side. Hence, the above equation becomes
$\Rightarrow 18l-15l=2430-2160$
Let us do the subtraction operation, we will get
$\Rightarrow 3l=270$
From this, we will get
$\Rightarrow l=\text{ }\dfrac{270}{3}=90$
Hence, the length of the train is $90$ meter.

So, the correct answer is “Option C”.

Note: In these types of questions, when the length of platform or anything such is given, we always add it to the length of the train. Here, you make errors by subtracting it or not even considering the platform length. You may write \[\text{ }\dfrac{l}{18}=\dfrac{l}{15}\] which when solved gives the length to be 0.