Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

Step 1: Understand the setup

• Speed of fast train = 40 km/hr
• Speed of slower train = 20 km/hr
• The man is sitting in the slower train, so his speed is also 20 km/hr
• Time taken to completely pass the man = 5 seconds

Step 2: Calculate relative speed

Relative speed = Speed of fast train - Speed of man
               = 40 - 20 = 20 km/hr
               = (20 × 1000) / 3600 = 5.56 m/s

Step 3: Use time and speed to calculate length of the train

Length = Relative speed × Time
       = 5.56 m/s × 5 s
       = 27.78 meters

Answer: The length of the fast train is approximately 27.78 meters.

This problem involves converting units and applying the basic distance = speed × time formula. Since both trains are moving in the same direction, we use the relative speed (difference in speeds). Questions like this are common in quantitative aptitude exams and help build understanding of relative motion.