Two trains run on parallel tracks at 126 kmph and 108 kmph. When they are running in opposite directions they cross each other completely in 5 seconds and when they are running in the same direction a passenger sitting in the faster train sees that the other train passes completely in 30 seconds. Then the length of the faster train is (in meters)    

Given:

Speed of faster train = 126 kmph = 126 × (5/18) = 35 m/s

Speed of slower train = 108 kmph = 108 × (5/18) = 30 m/s

Time when trains move in opposite direction = 5 sec

Time when trains move in same direction = 30 sec

Formula used:

Relative Speed (opposite) = sum of speeds

Relative Speed (same direction) = difference of speeds

Distance = Speed × Time

Calculation:

Relative speed (opposite) = 35 + 30 = 65 m/s

⇒ Total length = 65 × 5 = 325 m

Relative speed (same) = 35 - 30 = 5 m/s

⇒ Length of slower train = 5 × 30 = 150 m

⇒ Length of faster train = 325 - 150 = 175 m

∴ Length of the faster train = 175 meters