Question

A train of length $18{\text{0 m}}$ crosses a man standing on a platform in $12$ seconds and crosses another train coming from the opposite direction in ${\text{12 sec}}$ . If the second train runs at $\dfrac{2}{3}$ speed of the first then find the length of the second train?
A) $56$
B) $120$
C) $20$
D) $44$

Answer 1

Hint:
Here we use speed and time formulas for this given question, calculating the values on speed and time, finding the length of the second train and finding the speed of the first train.

Formula using:
${\text{Distance = speed \times time}}$

Complete step by step solution:
Length of the first train $ = 180m$
Time taken by the train to cross the man standing on the platform $ = 12s$
Speed of the first train $ = \dfrac{{{\text{length of the first train}}}}{{{\text{crossing time on the platform}}}}$
Speed of the first train $ = \dfrac{{180}}{{12}} = 15$
So, here speed of the first train is $15m/s$
Speed of the second train \[ = {\text{second train running speed \times speed of the first train = }}\dfrac{2}{3} \times 15 = 10\]
So, Speed of the second train is $10m/s$
Relative speed =speed of the first train $ + $Speed of the second train $ = 15 + 10 = 25$
Here, Relative speed is $25m/s$
Let the length of the train be $y$meters.
${\text{Distance = speed \times time}}$
$
  y + 180 = 25 \times 12 \\
  y + 180 = 300 \\
  y = 300 - 180 \\
  y = 120 \\
 $

Therefore, Length of the second train is $120m/s$. So, option $b$ is the correct answer in this question.

Additional information:
In this Question train crossed the opposite direction so we are using this method. Incase two trains are crossing in the same direction we will use another method. Then we are calculating step by step formulas and solution methods.

Note:
Here, we have a clear idea about how many train crossings the platform and what is the length of the train. We Calculate the speed of the second train and we will be clear about what is the speed of the first train. Here we will calculate distance, we will find the speed of the train and time taken by the train.