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Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?
- a)112, 78
- b)97.78, 55
- c)102.78, 50
- d)104.78, 55
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two trains are traveling in opposite directions at uniform speed 60 a...
Given Information:
- Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively.
- They take 5 seconds to cross each other.
- If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds.
To Find: Lengths of trains (in meters)
Assumption:
- Both the trains are of equal length.
- Distance covered by each train to cross each other is equal to the sum of their lengths.
Solution:
Let's assume the length of each train to be L meters.
Speed of the first train = 60 km/hour = (60 x 1000) / (60 x 60) = 50/3 m/s
Speed of the second train = 50 km/hour = (50 x 1000) / (60 x 60) = 25/9 m/s
When two trains are traveling in opposite directions:
Relative speed = Speed of the first train + Speed of the second train
= (50/3) + (25/9) = (175/9) m/s
Distance covered to cross each other = Length of first train + Length of second train
= 2L
Time taken to cross each other = 5 seconds
Therefore, 2L = (175/9) x 5
=> L = (175/9) x (5/2)
=> L = 102.78 meters
When two trains are traveling in the same direction:
Relative speed = Speed of the first train - Speed of the second train
= (50/3) - (25/9) = (125/9) m/s
As per the question, a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds.
Therefore, Distance covered by the faster train in 18 seconds = Distance covered by the slower train + Length of the slower train
=> (50/3) x 18 = (25/9) x t + 102.78
where t = time taken by the slower train to cover the distance of its length
=> t = (50/3) x 18 - 102.78 x (9/25)
=> t = 44.44 seconds
As we know, Speed = Distance / Time
Speed of the slower train = (25/9) m/s
Time taken by the slower train to cover its length = t = 44.44 seconds
Therefore, Length of the slower train = Speed x Time taken
= (25/9) x 44.44
= 102.78 meters
Hence, the lengths of the trains are 102.78 meters each.
Therefore, option (c) is the correct answer.
- Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively.
- They take 5 seconds to cross each other.
- If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds.
To Find: Lengths of trains (in meters)
Assumption:
- Both the trains are of equal length.
- Distance covered by each train to cross each other is equal to the sum of their lengths.
Solution:
Let's assume the length of each train to be L meters.
Speed of the first train = 60 km/hour = (60 x 1000) / (60 x 60) = 50/3 m/s
Speed of the second train = 50 km/hour = (50 x 1000) / (60 x 60) = 25/9 m/s
When two trains are traveling in opposite directions:
Relative speed = Speed of the first train + Speed of the second train
= (50/3) + (25/9) = (175/9) m/s
Distance covered to cross each other = Length of first train + Length of second train
= 2L
Time taken to cross each other = 5 seconds
Therefore, 2L = (175/9) x 5
=> L = (175/9) x (5/2)
=> L = 102.78 meters
When two trains are traveling in the same direction:
Relative speed = Speed of the first train - Speed of the second train
= (50/3) - (25/9) = (125/9) m/s
As per the question, a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds.
Therefore, Distance covered by the faster train in 18 seconds = Distance covered by the slower train + Length of the slower train
=> (50/3) x 18 = (25/9) x t + 102.78
where t = time taken by the slower train to cover the distance of its length
=> t = (50/3) x 18 - 102.78 x (9/25)
=> t = 44.44 seconds
As we know, Speed = Distance / Time
Speed of the slower train = (25/9) m/s
Time taken by the slower train to cover its length = t = 44.44 seconds
Therefore, Length of the slower train = Speed x Time taken
= (25/9) x 44.44
= 102.78 meters
Hence, the lengths of the trains are 102.78 meters each.
Therefore, option (c) is the correct answer.
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Community Answer
Two trains are traveling in opposite directions at uniform speed 60 a...
Let the lengths of the faster train and slower train be A and B respectively
When the trains are travelling in opposite direction, relative speed = 60 + 50 = 110 km/hour = 30.55 m/s
And they cross each other in 5 seconds
Hence, the total length of two trains = A + B = relative speed X time taken to cross each other
A + B = 30.55 X 5 = 152.78 metres
When the trains are travelling in the same direction, relative speed = 60 - 50 = 10 km/hour = 2.78 m/s
The distance covered by the passenger sitting in fast train to overtake the slower train is equal to the length of the slower train
Hence, distance covered by the passenger = length of the slower train = relative speed X time taken to overtake
B = 2.78 X 18 = 50 metres
Hence, the length of the faster train = 102.78 metres
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Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice Two trains are traveling in opposite directions at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had travelled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in meters)?a)112, 78b)97.78, 55c)102.78, 50d)104.78, 55e)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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