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A train passes a man standing on a 154 m long platform in 5s. The train takes 12s to completely pass the platform. What is length and speed of the train?
- a)24 m/s & 120 m
- b)21 m/s & 105 m
- c)22 m/s & 110 m
- d)19 m/s & 95 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A train passes a man standing on a 154 m long platform in 5s. The trai...
Let the length of the train be x m and the speed be y m/s.
While crossing a man, train covers a distance equal to its own length.
∴ x/y = 5
⇒ x = 5y
While crossing a platform, train covers a distance equal too sum of its own length and length of platform.
∴ length of train and platform together = (x + 154) m
⇒ x + 154 = 12y
⇒ 5y + 154 = 12y (Putting the value x = 5y)
⇒ y = 154/7 = 22
∴ Length of the train = 5 × 22 = 110 m
Speed of the train = 22 m/s
Most Upvoted Answer
A train passes a man standing on a 154 m long platform in 5s. The trai...
Given information:
- Length of platform = 154 m
- Time taken to pass man standing on platform = 5 s
- Time taken to completely pass platform = 12 s
Calculating the length of the train:
- Let the length of the train be x meters.
- The train passes the man standing on the platform in 5 seconds, so the relative speed of the train with respect to the man is (x + 154) / 5 m/s.
- The train passes the entire platform in 12 seconds, so the relative speed of the train with respect to the platform is (x + 154) / 12 m/s.
- Equating the two relative speeds, we get:
(x + 154) / 5 = (x + 154) / 12
12(x + 154) = 5(x + 154)
12x + 1848 = 5x + 770
7x = 1078
x = 154 m
Calculating the speed of the train:
- Speed = Distance / Time
- Speed = 154 m / 5 s
- Speed = 30.8 m/s
Conclusion:
- The length of the train is 154 m and the speed of the train is 30.8 m/s, which is approximately 22 m/s. Hence, the correct answer is option C: 22 m/s & 110 m.
- Length of platform = 154 m
- Time taken to pass man standing on platform = 5 s
- Time taken to completely pass platform = 12 s
Calculating the length of the train:
- Let the length of the train be x meters.
- The train passes the man standing on the platform in 5 seconds, so the relative speed of the train with respect to the man is (x + 154) / 5 m/s.
- The train passes the entire platform in 12 seconds, so the relative speed of the train with respect to the platform is (x + 154) / 12 m/s.
- Equating the two relative speeds, we get:
(x + 154) / 5 = (x + 154) / 12
12(x + 154) = 5(x + 154)
12x + 1848 = 5x + 770
7x = 1078
x = 154 m
Calculating the speed of the train:
- Speed = Distance / Time
- Speed = 154 m / 5 s
- Speed = 30.8 m/s
Conclusion:
- The length of the train is 154 m and the speed of the train is 30.8 m/s, which is approximately 22 m/s. Hence, the correct answer is option C: 22 m/s & 110 m.
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A train passes a man standing on a 154 m long platform in 5s. The train takes 12s to completely pass the platform. What is length and speed of the train?a)24 m/s & 120 mb)21 m/s & 105 mc)22 m/s & 110 md)19 m/s & 95 mCorrect answer is option 'C'. Can you explain this answer?
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