A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train is :

90 m

Speed = \(\frac{ Distance}{ Time}\)

Let the length of the train be x

According to the question,

Speed = \(\frac{\text{x + 162}}{ 18}\) -------1st equation

Speed = \(\frac{\text{x + 120}}{ 15}\) -------2nd equation

Therefore, we can say that:

\(\frac{\text{x + 162}}{ 18}\) = \(\frac{\text{x + 120}}{ 15}\)

\(\frac{\text{x + 162}}{ 6}\) = \(\frac{\text{x + 120}}{ 5}\)

5x + 810 = 6x + 720

x = 90

So, the length of train is 90 m