Trains P and Q move along parallel tracks in the same direction. Train P completely overtakes the train Q in 60 seconds, and a passenger in the train P crosses train Q in 40 seconds. If the trains have their speeds in the ratio 2 : 1, what is the ratio of their lengths?

Correct option is D

Given:
Train P overtakes Train Q in 60 seconds.
A passenger in Train P crosses Train Q in 40 seconds.
Speed ratio of Trains P and Q = 2:1
Formula Used:
Relative speed when both trains move in the same direction = Speed of P - Speed of Q
Length of Train P + Length of Train Q = Relative Speed ×\times× Time for overtaking
Length of Train P = Relative Speed × Time for passenger crossing
Solution:
Let the length of train P and Q be the x and y.
Let the speed of the P and Q train is 2z and z respectively.
As per the question, both train running on the same direction
Relative speed = 2z-z= z
(x+y)/60 = z (1)
y/40 = z (2)
from eqn. 1 and 2 we get
x/y= ½
so x:y = 1:2