A boy runs opposite to that of a train at a speed of 25 km/hr. If the relative…
2023
A boy runs opposite to that of a train at a speed of 25 km/hr. If the relative speed between the train and the boy running in the opposite direction is 60 km/hr. What is the length of the train, if it takes 90 seconds to cross the boy, when he is at rest?
- A.
193.2 m
- B.
194.4 m
- C.
192.6 m
- D.
191.8 m
Attempted by 11 students.
Show answer & explanation
Correct answer: B
Step 1: Find the train's speed relative to ground
Relative speed between the train and the boy running in the opposite direction is 60 km/h. The boy's speed is 25 km/h, so the train's speed = 60 − 25 = 35 km/h.
Step 2: Convert the train speed to m/s
35 km/h = 35 × (5/18) m/s = 175/18 ≈ 9.722... m/s.
Step 3: Use crossing time to find the train length
The provided answer choices correspond to using a crossing time of 20 seconds. (If the problem were using 90 seconds as written, the computed length would be much larger — see note below.)
Length = speed × time = 9.722... m/s × 20 s ≈ 194.444... m ≈ 194.4 m.
Final answer: 194.4 m
Note: If the crossing time were actually 90 seconds as stated, length = 9.722... × 90 ≈ 875 m, which does not match the provided options. Therefore to match the options the crossing time must be 20 s; the problem text likely contains a typo.