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Two trains running at speeds of 36 kmph and 54 kmph, respectively cross each other in 10 sec, if they run in opposite directions. When they run in the same direction, a person sitting in the faster train observes that he crossed the other train in 20 seconds. Find the lengths of the two trains.
- a)200 m, 50 m
- b)100 m, 150 m
- c)180 m, 70 m
- d)125 m, 125 m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two trains running at speeds of 36 kmph and 54 kmph, respectively cros...
Let length of slower train-1 be L1 and length of faster train-2 be L2.
Relative speed when trains run in opposite directions = (54 + 36) × 5/18 = 25 m/s
So, 10 = (L1 + L2)/25
Relative speed when trains run in the same direction = (54 - 36)
Now,
20 = L1/5
L1 = 100 m ..........(2)
Relative speed when trains run in opposite directions = (54 + 36) × 5/18 = 25 m/s
So, 10 = (L1 + L2)/25
L
1 + L
2 = 250 ........(1)
Relative speed when trains run in the same direction = (54 - 36)
×
5/18 = 5 m/sNow,
20 = L1/5
L1 = 100 m ..........(2)
Put (2) in (1),
L
2 = 150 m
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Community Answer
Two trains running at speeds of 36 kmph and 54 kmph, respectively cros...
Let's assume the lengths of the two trains are L1 and L2 respectively.
When the trains are running in opposite directions:
- The relative speed of the trains is the sum of their individual speeds, which is (36 + 54) kmph = 90 kmph.
- The time taken to cross each other is given as 10 seconds.
- The distance covered by both trains in 10 seconds is equal to the sum of their lengths, which is (L1 + L2).
Using the formula distance = speed × time, we can write the equation as:
90 kmph × (10/3600) hours = L1 + L2
Simplifying the equation, we have:
(90 × 10) / 3600 = L1 + L2
L1 + L2 = 0.25
When the trains are running in the same direction:
- The relative speed of the trains is the difference between their individual speeds, which is (54 - 36) kmph = 18 kmph.
- The time taken by the faster train to cross the slower train is given as 20 seconds.
- The distance covered by the faster train in 20 seconds is equal to the difference in lengths of the two trains, which is (L1 - L2).
Using the formula distance = speed × time, we can write the equation as:
18 kmph × (20/3600) hours = L1 - L2
Simplifying the equation, we have:
(18 × 20) / 3600 = L1 - L2
L1 - L2 = 0.1
Now we have two equations:
L1 + L2 = 0.25
L1 - L2 = 0.1
Solving these equations simultaneously, we can find the lengths of the two trains:
Adding the two equations, we have:
2L1 = 0.35
L1 = 0.35/2 = 0.175
Substituting the value of L1 into the first equation, we have:
0.175 + L2 = 0.25
L2 = 0.25 - 0.175 = 0.075
Converting the lengths from km to meters, we have:
L1 = 0.175 km × 1000 m/km = 175 m
L2 = 0.075 km × 1000 m/km = 75 m
Therefore, the lengths of the two trains are 175 meters and 75 meters respectively.
When the trains are running in opposite directions:
- The relative speed of the trains is the sum of their individual speeds, which is (36 + 54) kmph = 90 kmph.
- The time taken to cross each other is given as 10 seconds.
- The distance covered by both trains in 10 seconds is equal to the sum of their lengths, which is (L1 + L2).
Using the formula distance = speed × time, we can write the equation as:
90 kmph × (10/3600) hours = L1 + L2
Simplifying the equation, we have:
(90 × 10) / 3600 = L1 + L2
L1 + L2 = 0.25
When the trains are running in the same direction:
- The relative speed of the trains is the difference between their individual speeds, which is (54 - 36) kmph = 18 kmph.
- The time taken by the faster train to cross the slower train is given as 20 seconds.
- The distance covered by the faster train in 20 seconds is equal to the difference in lengths of the two trains, which is (L1 - L2).
Using the formula distance = speed × time, we can write the equation as:
18 kmph × (20/3600) hours = L1 - L2
Simplifying the equation, we have:
(18 × 20) / 3600 = L1 - L2
L1 - L2 = 0.1
Now we have two equations:
L1 + L2 = 0.25
L1 - L2 = 0.1
Solving these equations simultaneously, we can find the lengths of the two trains:
Adding the two equations, we have:
2L1 = 0.35
L1 = 0.35/2 = 0.175
Substituting the value of L1 into the first equation, we have:
0.175 + L2 = 0.25
L2 = 0.25 - 0.175 = 0.075
Converting the lengths from km to meters, we have:
L1 = 0.175 km × 1000 m/km = 175 m
L2 = 0.075 km × 1000 m/km = 75 m
Therefore, the lengths of the two trains are 175 meters and 75 meters respectively.
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Two trains running at speeds of 36 kmph and 54 kmph, respectively cross each other in 10 sec, if they run in opposite directions. When they run in the same direction, a person sitting in the faster train observes that he crossed the other train in 20 seconds. Find the lengths of the two trains.a)200 m, 50 mb)100 m, 150 mc)180 m, 70 md)125 m, 125 mCorrect answer is option 'B'. Can you explain this answer?
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Two trains running at speeds of 36 kmph and 54 kmph, respectively cross each other in 10 sec, if they run in opposite directions. When they run in the same direction, a person sitting in the faster train observes that he crossed the other train in 20 seconds. Find the lengths of the two trains.a)200 m, 50 mb)100 m, 150 mc)180 m, 70 md)125 m, 125 mCorrect answer is option 'B'. 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 running at speeds of 36 kmph and 54 kmph, respectively cross each other in 10 sec, if they run in opposite directions. When they run in the same direction, a person sitting in the faster train observes that he crossed the other train in 20 seconds. Find the lengths of the two trains.a)200 m, 50 mb)100 m, 150 mc)180 m, 70 md)125 m, 125 mCorrect answer is option 'B'. 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 running at speeds of 36 kmph and 54 kmph, respectively cross each other in 10 sec, if they run in opposite directions. When they run in the same direction, a person sitting in the faster train observes that he crossed the other train in 20 seconds. Find the lengths of the two trains.a)200 m, 50 mb)100 m, 150 mc)180 m, 70 md)125 m, 125 mCorrect answer is option 'B'. Can you explain this answer?.
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