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A train travelling at 48 km/hr crosses another train, having half its length and travelling in opposite direction at 42 km/hr in 12 seconds. It also passed a railway platform in 45 seconds. The length of the rail platform is
- a)200 m
- b)300 m
- c)350 m
- d)400 m
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Problem
To find the length of the railway platform, we first need to determine the lengths of the two trains involved in the scenario.
Step 1: Calculate the Length of the First Train
- Speed of the first train = 48 km/hr = \( \frac{48 \times 1000}{3600} = 13.33 \) m/s
- Speed of the second train = 42 km/hr = \( \frac{42 \times 1000}{3600} = 11.67 \) m/s
- Combined speed when crossing each other = \( 13.33 + 11.67 = 25 \) m/s
- Time taken to cross each other = 12 seconds
- Distance covered when crossing each other = Speed \( \times \) Time
- Distance = \( 25 \, \text{m/s} \times 12 \, \text{s} = 300 \, \text{m} \)
- Let the length of the first train be \( L \) meters. The second train is half its length, or \( \frac{L}{2} \) meters. Thus:
- \( L + \frac{L}{2} = 300 \)
- \( \frac{3L}{2} = 300 \)
- \( L = 200 \) meters
Step 2: Calculate the Length of the Platform
- The total time taken to pass the platform = 45 seconds.
- Speed of the first train remains 13.33 m/s.
- Distance covered while passing the platform = Speed \( \times \) Time
- Distance = \( 13.33 \, \text{m/s} \times 45 \, \text{s} = 600 \, \text{m} \)
- This distance includes the length of the first train and the railway platform:
- Length of the platform = Total distance - Length of the first train
- Length of the platform = \( 600 \, \text{m} - 200 \, \text{m} = 400 \, \text{m} \)
Conclusion
Thus, the length of the railway platform is 400 meters, confirming that the correct answer is option D.
To find the length of the railway platform, we first need to determine the lengths of the two trains involved in the scenario.
Step 1: Calculate the Length of the First Train
- Speed of the first train = 48 km/hr = \( \frac{48 \times 1000}{3600} = 13.33 \) m/s
- Speed of the second train = 42 km/hr = \( \frac{42 \times 1000}{3600} = 11.67 \) m/s
- Combined speed when crossing each other = \( 13.33 + 11.67 = 25 \) m/s
- Time taken to cross each other = 12 seconds
- Distance covered when crossing each other = Speed \( \times \) Time
- Distance = \( 25 \, \text{m/s} \times 12 \, \text{s} = 300 \, \text{m} \)
- Let the length of the first train be \( L \) meters. The second train is half its length, or \( \frac{L}{2} \) meters. Thus:
- \( L + \frac{L}{2} = 300 \)
- \( \frac{3L}{2} = 300 \)
- \( L = 200 \) meters
Step 2: Calculate the Length of the Platform
- The total time taken to pass the platform = 45 seconds.
- Speed of the first train remains 13.33 m/s.
- Distance covered while passing the platform = Speed \( \times \) Time
- Distance = \( 13.33 \, \text{m/s} \times 45 \, \text{s} = 600 \, \text{m} \)
- This distance includes the length of the first train and the railway platform:
- Length of the platform = Total distance - Length of the first train
- Length of the platform = \( 600 \, \text{m} - 200 \, \text{m} = 400 \, \text{m} \)
Conclusion
Thus, the length of the railway platform is 400 meters, confirming that the correct answer is option D.
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A train travelling at 48 km/hr crosses another train, having half its length and travelling in opposite direction at 42 km/hr in 12 seconds. It also passed a railway platform in 45 seconds. The length of the rail platformisa)200 mb)300 mc)350 md)400 me)None of theseCorrect answer is option 'D'. Can you explain this answer?
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