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From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?
- a)210 and 140
- b)162.5 and 187.5
- c)245 and 130
- d)175 and 200
Correct answer is option 'D'. Can you explain this answer?
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To solve this problem, let's assume the length of the train is 'x' meters and the length of the platform is 'y' meters.
1. Time taken for the train to completely pass through the platform:
Given that it takes 25 seconds for the back of the train to leave the platform, we can determine the time taken for the front of the train to enter the platform. Since the train is moving at a constant speed of 54 km/h, we can convert this to m/s by using the formula: speed in m/s = (speed in km/h) * (1000/3600).
Therefore, the speed of the train is 54 * (1000/3600) = 15 m/s.
So, the time taken for the front of the train to enter the platform is also 25 seconds.
Hence, the total time taken for the train to pass through the platform is 25 + 25 = 50 seconds.
2. Length of the train:
The distance covered by the train in 50 seconds is the sum of the length of the train and the length of the platform. Since the train is traveling at a constant speed, we can use the formula: distance = speed * time.
Therefore, the distance covered by the train is 15 * 50 = 750 meters.
Since the length of the platform is y meters, the length of the train is (750 - y) meters.
3. Time taken to pass the man:
Given that it takes 14 seconds for the train to pass a man running at 9 km/h in the same direction, we can determine the relative speed between the train and the man. The relative speed is the difference in their speeds.
The relative speed is (54 - 9) km/h = 45 km/h.
Converting this to m/s, the relative speed is 45 * (1000/3600) = 12.5 m/s.
Using the formula: distance = speed * time, we can determine the distance covered by the train in 14 seconds.
Therefore, the distance covered by the train is 12.5 * 14 = 175 meters.
4. Length of the platform:
From the above calculations, we know that the distance covered by the train in 50 seconds is 750 meters and the distance covered by the train in 14 seconds is 175 meters. The difference between these distances is the length of the platform.
Hence, the length of the platform is 750 - 175 = 575 meters.
Therefore, the length of the train is 750 - 575 = 175 meters and the length of the platform is 575 meters. Hence, the correct answer is option 'D'.
1. Time taken for the train to completely pass through the platform:
Given that it takes 25 seconds for the back of the train to leave the platform, we can determine the time taken for the front of the train to enter the platform. Since the train is moving at a constant speed of 54 km/h, we can convert this to m/s by using the formula: speed in m/s = (speed in km/h) * (1000/3600).
Therefore, the speed of the train is 54 * (1000/3600) = 15 m/s.
So, the time taken for the front of the train to enter the platform is also 25 seconds.
Hence, the total time taken for the train to pass through the platform is 25 + 25 = 50 seconds.
2. Length of the train:
The distance covered by the train in 50 seconds is the sum of the length of the train and the length of the platform. Since the train is traveling at a constant speed, we can use the formula: distance = speed * time.
Therefore, the distance covered by the train is 15 * 50 = 750 meters.
Since the length of the platform is y meters, the length of the train is (750 - y) meters.
3. Time taken to pass the man:
Given that it takes 14 seconds for the train to pass a man running at 9 km/h in the same direction, we can determine the relative speed between the train and the man. The relative speed is the difference in their speeds.
The relative speed is (54 - 9) km/h = 45 km/h.
Converting this to m/s, the relative speed is 45 * (1000/3600) = 12.5 m/s.
Using the formula: distance = speed * time, we can determine the distance covered by the train in 14 seconds.
Therefore, the distance covered by the train is 12.5 * 14 = 175 meters.
4. Length of the platform:
From the above calculations, we know that the distance covered by the train in 50 seconds is 750 meters and the distance covered by the train in 14 seconds is 175 meters. The difference between these distances is the length of the platform.
Hence, the length of the platform is 750 - 175 = 575 meters.
Therefore, the length of the train is 750 - 575 = 175 meters and the length of the platform is 575 meters. Hence, the correct answer is option 'D'.
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From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer?
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From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer?.
From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?a)210 and 140b)162.5 and 187.5c)245 and 130d)175 and 200Correct answer is option 'D'. Can you explain this answer?.
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