Two trains running at the rates of 75 and 60 kmph respectively, On parallel rails in opposite directions, are observed to pass each other in 12 seconds, and when they are running in the same direction at the same rate as before, a person sitting in the faster train observes that he passes the other in 90 seconds. Find the lengths of the trains

Let the length of the slower and Faster train be x and y respectively Now relative speed of train when travelling opposite direction = 75 + 60 = 135 km/hr = 135 × (5/18) m/s= 37.5 m/s Now distance covered (x) = 37.5 × 12 = 450 m ......................... (i) When travelling in same direction, relative speed = 75 – 60 = 15 km/hr = 15 × (5/18) m/s= 75/18 m/s As the time noted by the person in the faster is 90 seconds, the distance covered will be equal to the length of slower train Distance covered (y) = 75/18 × 90 = 375m ................................... (ii) From (i) and (ii) we get x= 75m