Question

A train crosses a 340m long platform in 30 seconds whereas it crosses a 370m long platform in 32 seconds. Find its length (in m).
(a) 130
(b) 100
(c) 120
(d) 110

Answer 1

We will first assume the length of the train to be ‘l’ metre. Then we will use a formula of speed which is given as $speed=\dfrac{\text{distance}}{\text{time}}$ where distance will be addition of length of platform and length of train. So, we will get two equation as $\dfrac{\left( 340+l \right)}{30}\dfrac{m}{s}$ and $\dfrac{\left( 370+l \right)}{32}\dfrac{m}{s}$ . On simplification, we will get length of train.

Complete step-by-step answer:
Here, we know that the as compared to platform length of train is more. We will assume the length of the train to be let say variable l. So, we are given that the length of the platform is 340m So, we can say that the length of the train will be $\left( 340+l \right)m$ . Similarly, the length of the train for a 370m long platform will be $\left( 370+l \right)m$ .
So, we are given that the train crossed a 340m long platform in 30 sec. We can write the speed of the train in mathematical form as $\dfrac{\left( 340+l \right)}{30}\dfrac{m}{s}$ . Similarly, for a 370m long platform train takes 32seconds, we can write it as $\dfrac{\left( 370+l \right)}{32}\dfrac{m}{s}$ .
We will equate both he equation to find length of train l. so, we write it as
$\dfrac{\left( 370+l \right)}{32}=\dfrac{\left( 340+l \right)}{30}$
On further solving, we will get equation as
$\dfrac{\left( 370+l \right)}{16}=\dfrac{\left( 340+l \right)}{15}$
On simplification we will get,
$\left( 370+l \right)15=\left( 340+l \right)16$
On multiplying the brackets, we will get
$5550+15l=5440+16l$
$5550-5440=16l-15l$
$\therefore l=110m$
Thus, the length of the train is 110m.
Hence, option (d) is correct.

Note: In this type of tricky question, which formula is to be used should be known by seeing the units given in question. Otherwise using any other formula will result in the wrong answer. Also, do not subtract length of train from the length of platform i.e. $\dfrac{\left( 370-l \right)}{16}=\dfrac{\left( 340-l \right)}{15}$ . This is a wrong concept and the answer will not be correct. So, do not make this mistake.