A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

Given Data

• Two walkers moving in the same direction at 2 km/hr and 4 km/hr
• Train passes them completely in 9 s and 10 s respectively
• Required: length of the train

Step 1: Let train speed = v km/hr and length = L m
Relative speed with first walker = (v − 2) km/hr = (v − 2) × (5/18) m/sL = 9 × (v − 2) × (5/18) = (5/2)(v − 2)

Step 2: Use second walker
Relative speed = (v − 4) × (5/18) m/sL = 10 × (v − 4) × (5/18) = (25/9)(v − 4)

Step 3: Equate L from both cases
(5/2)(v − 2) = (25/9)(v − 4)⇒ 45(v − 2) = 50(v − 4)⇒ 45v − 90 = 50v − 200 ⇒ 5v = 110 ⇒ v = 22 km/hrThen L = (5/2)(22 − 2) = (5/2) × 20 = 50 m

Checks & Common Pitfalls

• Same direction ⇒ use difference of speeds.
• When passing a person, distance equals only the train length.
• Keep conversions consistent (km/hr ↔ m/s).

Final Answer
The train's length is 50 m.