Two trains are running at 40 km/h and 20 km/h respectively in the same direction on parallel tracks. The faster train completely passes a man sitting in the slower train in 5 seconds. What is the length of the faster train in metres?

Introduction / Context:
This question again uses the concept of relative speed for two trains moving in the same direction. The goal is to use the time taken for the faster train to overtake a man sitting in the slower train to compute the length of the faster train. The presence of mixed fraction options hints that the exact answer is a repeating decimal that is more neatly expressed as a fraction.

Given Data / Assumptions:

• Speed of faster train = 40 km/h.
• Speed of slower train (where the man is sitting) = 20 km/h.
• Time taken for the faster train to pass the man completely = 5 s.
• Both trains travel in the same direction on parallel tracks with constant speeds.
• The man is treated as a point object.

Concept / Approach:
The effective speed of the faster train relative to the man is the difference of their speeds, since they move in the same direction. Once we convert this relative speed to m/s, the length of the faster train is simply the product of the relative speed and the overtaking time. The result will be a fraction, which we can convert into a mixed fraction format to match the options.

Step-by-Step Solution:
Relative speed in km/h = 40 − 20 = 20 km/h. Convert to m/s: 20 * (5 / 18) = 100 / 18 = 50 / 9 m/s. Time to pass the man = 5 s. Length of faster train = relative speed * time = (50 / 9) * 5 = 250 / 9 m. 250 / 9 = 27 remainder 7, so 27 7/9 m.

Verification / Alternative check:
Check by reversing: at relative speed 50 / 9 m/s, a length of 250 / 9 m will take (250 / 9) / (50 / 9) = 5 s to pass, which matches the given time exactly. This confirms that the calculation and fractional form are correct.

Why Other Options Are Wrong:
Values like 25 8/7 m, 21 1/4 m or 22 m do not equal 250 / 9 m when converted to improper fractions. Using those lengths with the same relative speed would give times different from 5 s, so they cannot satisfy the given condition of the question.

Common Pitfalls:
A major pitfall is using the sum of the two speeds instead of the difference, which is only valid for opposite directions. Another error is to round the fraction 250 / 9 too early, which can lead to confusion when comparing with fractional options. Keeping the exact fraction until the end makes it easy to recognize the correct mixed number.

Final Answer:
The length of the faster train is 27 7/9 m.