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A train of length 500 m crosses a platform in 50 sec and another train of the same length, moving in the opposite direction with double the speed of the first train, crosses a pole in 20 sec. What is the length of the platform?
- a)500 m
- b)250 m
- c)125 m
- d)625 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A train of length 500 m crosses a platform in 50 sec and another train...
Assume length of platform = L metres
Speed of first train = V m/sec
According to the given condition,
50V = L + 500
Speed of second train = 500/20 = 25 m/sec
Therefore, speed of first train = 12.5 m/sec
Hence, length of platform = 50 × 12.5 - 500 = 625 - 500 = 125 m
Speed of first train = V m/sec
According to the given condition,
50V = L + 500
Speed of second train = 500/20 = 25 m/sec
Therefore, speed of first train = 12.5 m/sec
Hence, length of platform = 50 × 12.5 - 500 = 625 - 500 = 125 m
Most Upvoted Answer
A train of length 500 m crosses a platform in 50 sec and another train...
Let's assume the speed of the first train is x m/s.
Given that the length of the train is 500 m and it crosses the platform in 50 seconds, we can use the formula:
Speed = Distance/Time
So, the speed of the first train is:
x = 500/50
x = 10 m/s
Now, let's assume the length of the platform is y meters.
We are given that the second train is moving in the opposite direction with double the speed of the first train. So, the speed of the second train is 2x = 2 * 10 = 20 m/s.
The second train crosses a pole, so the distance covered by the second train is the length of the train itself, which is 500 meters.
Using the formula:
Speed = Distance/Time
20 = 500/20
20 = 25
So, it takes 25 seconds for the second train to cross the pole.
Now, let's calculate the time it takes for the second train to cross the platform.
The relative speed between the two trains is the sum of their speeds, which is 10 + 20 = 30 m/s.
Using the formula:
Speed = Distance/Time
30 = (500 + y)/t
30t = 500 + y
We are given that the time taken by the second train to cross the platform is 20 seconds, so t = 20.
Substituting the value of t, we get:
30 * 20 = 500 + y
600 = 500 + y
y = 600 - 500
y = 100
Therefore, the length of the platform is 100 meters.
Hence, the correct answer is option C) 125 m.
Given that the length of the train is 500 m and it crosses the platform in 50 seconds, we can use the formula:
Speed = Distance/Time
So, the speed of the first train is:
x = 500/50
x = 10 m/s
Now, let's assume the length of the platform is y meters.
We are given that the second train is moving in the opposite direction with double the speed of the first train. So, the speed of the second train is 2x = 2 * 10 = 20 m/s.
The second train crosses a pole, so the distance covered by the second train is the length of the train itself, which is 500 meters.
Using the formula:
Speed = Distance/Time
20 = 500/20
20 = 25
So, it takes 25 seconds for the second train to cross the pole.
Now, let's calculate the time it takes for the second train to cross the platform.
The relative speed between the two trains is the sum of their speeds, which is 10 + 20 = 30 m/s.
Using the formula:
Speed = Distance/Time
30 = (500 + y)/t
30t = 500 + y
We are given that the time taken by the second train to cross the platform is 20 seconds, so t = 20.
Substituting the value of t, we get:
30 * 20 = 500 + y
600 = 500 + y
y = 600 - 500
y = 100
Therefore, the length of the platform is 100 meters.
Hence, the correct answer is option C) 125 m.
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A train of length 500 m crosses a platform in 50 sec and another train of the same length, moving in the opposite direction with double the speed of the first train, crosses a pole in 20 sec. What is the length of the platform?a)500 mb)250 mc)125 md)625 mCorrect answer is option 'C'. Can you explain this answer?
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