Train A crosses a 230 meters long platform in 29 seconds and train B crosses a…
2024
Train A crosses a 230 meters long platform in 29 seconds and train B crosses a 150 meters long platform in 24 seconds. Train B having length of 450 meters crosses train A in 160 seconds, while running in the same direction. Find how much time will the train A take to cross a 50 meters long bridge (Speed of train B > speed of train A)?
- A.
16 seconds
- B.
22 seconds
- C.
20 seconds
- D.
17 seconds
- E.
25 seconds
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
When a train crosses a stationary object (platform or bridge), the distance covered equals the train's own length plus the object's length, and time = distance / speed. When one train crosses another while both move in the same direction, the effective distance is the sum of their lengths and the effective speed is the difference of their speeds (relative speed).
Application
Speed of train B: B is 450 m long and crosses a 150 m platform, so it covers 450 + 150 = 600 m in 24 s, giving speed of B = 600 / 24 = 25 m/s.
Length of train A in terms of its speed: A crosses a 230 m platform in 29 s, so length of A + 230 = 29 x (speed of A).
Same-direction crossing: B crosses A in 160 s, covering (450 + length of A) at relative speed (25 - speed of A). So 450 + length of A = 160 x (25 - speed of A).
Substitute length of A = 29 x (speed of A) - 230: 450 + 29 x (speed of A) - 230 = 4000 - 160 x (speed of A), i.e. 220 + 29 x (speed of A) = 4000 - 160 x (speed of A).
Collect terms: 189 x (speed of A) = 3780, so speed of A = 20 m/s, and length of A = 29 x 20 - 230 = 350 m.
Time for A to cross a 50 m bridge = (350 + 50) / 20 = 400 / 20 = 20 seconds.
Cross-check
With speed of A = 20 m/s and speed of B = 25 m/s, relative speed = 5 m/s and combined length = 450 + 350 = 800 m, so B crosses A in 800 / 5 = 160 s, matching the given data. Also speed of B (25) > speed of A (20), consistent with the stated condition.