Train 'P' can cross a pole in 8 seconds, while train 'Q' takes 15 seconds to cross train 'P' when they travel in opposite directions on parallel tracks. If the ratio of length of train 'P' to that of train 'Q' is 2:3 and the speed of train 'P' is 54 km/h, then find the speed (in km/h) of train 'Q'.
Show answer & explanation
Correct answer: D
Explanation
Given:
P passes a pole = 8 seconds
Speed of P = 54 km/h
Length of P : Q = 2 : 3
Time to cross each other in opposite directions = 15 seconds
54 km/h = 54 × 5/18 = 15 m/s
Length of P = 15 × 8 = 120 m
Length ratio
P : Q = 2 : 3
Length of Q = (3/2) × 120 = 180 m
Total distance in opposite directions = 120 + 180 = 300 m
Total speed = 300 / 15 = 20 m/s
Speed of Q = 20 − 15 = 5 m/s
Speed in km/h = 5 × 18 / 5 = 18
Speed of train Q = 18 km/h.