Question

A train can cross $340m$ long platform in $30$ seconds whereas it can cross a $370m$ long platform in $32$ seconds. Find its length in meters.
A. $130$
B. $100$
C. $120$
D. $110$

Answer 1

Hint: 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 $=340m$ . So, the length of the train can be written as $(340+l)m$ . Similarly, the length of the train crossing the $370m$ long platform is $(370+l)m$ . We will use the formula, $\text{Speed}=\text{ }\dfrac{\text{Distance}}{\text{Time}}$ . We will substitute the values of each platform case in this equation. Since the speed of the train is constant, let us equate these two equations, that is, $\text{ }\dfrac{\text{340}+l}{30}=\text{ }\dfrac{\text{370}+l}{32}$ . 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 $=340m$ .
Hence, the length of the train can be written as $(340+l)m$ .
We know that $\text{Speed}=\text{ }\dfrac{\text{Distance}}{\text{Time}}$
It is given that the train crosses $340m$ long platform in $30$ seconds .
So, let us write the above equation as
$\text{Speed}=\text{ }\dfrac{\text{340}+l}{30}...(i)$
It is also given that the train crosses a $370m$ long platform in $32$ seconds.
From, this we get the length of the train as $(370+l)m$ and the speed can be written as
$\text{Speed}=\text{ }\dfrac{\text{370}+l}{32}...(ii)$
The speed of the train is constant. Hence, we can equate the equations $(i)$ and $(ii)$ .
Hence, we get
$\text{ }\dfrac{\text{340}+l}{30}=\text{ }\dfrac{\text{370}+l}{32}$
Let us solve the equation to get the value of $l$ .
$32(\text{340}+l)=\text{ }30(\text{370}+l)$
Let us do the multiplication operation. We will get
$10880+32l=\text{ }11100+30l$
Let us collect constants to one side. We will get
$32l-30l=\text{ }11100-10880$
Doing the subtraction operation, we will get
$2l=\text{ }220$
From this, we will get
$l=\text{ }\dfrac{220}{2}=110$
Hence, the length of the train is $110$ meter.

So, the correct answer is “Option D”.

Note:
Be aware of the units given in the question. We added the length of the train to the platform length. Do not subtract the length of the train from the platform length, for example, $(340-l)m$ . The equation of speed should be thorough. In these types of questions, the speed of the train will not be given. We will have to assume the speed to be constant as the same train crosses the different platforms.