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Two trains, whose respective lengths are 120 metres and 180 metres, cross each other in 15 seconds when they are moving in opposite directions and in 50 seconds when they are moving in the same direction. What is the speed of the faster train (in km/hr)?
- a)46.8 kmph
- b)40.2 kmph
- c)54 kmph
- d)56.5 kmph
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two trains, whose respective lengths are 120 metres and 180 metres, c...
Let the speed of faster train be x and
speed of slower train be y
According to question,
when they are moving in opposite direction
(x + y) = (180 + 120)/15
(x + y) = 300/15
(x + y) = 20 .................(i)
now, when they are moving same direction
(x - y) = (180 + 120)/50
(x - y) = 300/50
(x - y) = 6....................(ii)
from (i) and (ii), we get
x = 13 m/sec and y = 7 m/sec
therefore, Speed of faster train (in km/hr) = 13 × (18/5)
= 46.8 km/hr
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Community Answer
Two trains, whose respective lengths are 120 metres and 180 metres, c...
To solve this question, we can use the concept of relative speed.
Let's assume the speeds of the two trains are v1 and v2, where v1 is the speed of the faster train.
When the trains are moving in opposite directions:
- The length of both trains combined is 120 + 180 = 300 meters.
- The relative speed of the trains is the sum of their individual speeds, which is v1 + v2.
- The time taken to cross each other is 15 seconds.
Using the formula: Distance = Speed × Time, we can write the equation:
300 = (v1 + v2) × 15
When the trains are moving in the same direction:
- The length of one train needs to be covered by the other train to cross it.
- The relative speed of the trains is the difference between their individual speeds, which is v1 - v2.
- The time taken to cross each other is 50 seconds.
Using the formula: Distance = Speed × Time, we can write the equation:
180 = (v1 - v2) × 50
Now, we have two equations with two variables (v1 and v2). We can solve these equations simultaneously to find the values of v1 and v2.
Solving equation 1:
300 = (v1 + v2) × 15
Dividing both sides by 15:
20 = v1 + v2
Solving equation 2:
180 = (v1 - v2) × 50
Dividing both sides by 50:
3.6 = v1 - v2
Adding equation 1 and 2:
20 + 3.6 = v1 + v2 + v1 - v2
23.6 = 2v1
Dividing both sides by 2:
v1 = 23.6 / 2
v1 = 11.8 m/s
To convert the speed from meters per second to kilometers per hour, we multiply by 18/5:
v1 = 11.8 × 18/5
v1 = 42.48 km/hr
Therefore, the speed of the faster train is approximately 42.48 km/hr, which is closest to option A (46.8 km/hr).
Let's assume the speeds of the two trains are v1 and v2, where v1 is the speed of the faster train.
When the trains are moving in opposite directions:
- The length of both trains combined is 120 + 180 = 300 meters.
- The relative speed of the trains is the sum of their individual speeds, which is v1 + v2.
- The time taken to cross each other is 15 seconds.
Using the formula: Distance = Speed × Time, we can write the equation:
300 = (v1 + v2) × 15
When the trains are moving in the same direction:
- The length of one train needs to be covered by the other train to cross it.
- The relative speed of the trains is the difference between their individual speeds, which is v1 - v2.
- The time taken to cross each other is 50 seconds.
Using the formula: Distance = Speed × Time, we can write the equation:
180 = (v1 - v2) × 50
Now, we have two equations with two variables (v1 and v2). We can solve these equations simultaneously to find the values of v1 and v2.
Solving equation 1:
300 = (v1 + v2) × 15
Dividing both sides by 15:
20 = v1 + v2
Solving equation 2:
180 = (v1 - v2) × 50
Dividing both sides by 50:
3.6 = v1 - v2
Adding equation 1 and 2:
20 + 3.6 = v1 + v2 + v1 - v2
23.6 = 2v1
Dividing both sides by 2:
v1 = 23.6 / 2
v1 = 11.8 m/s
To convert the speed from meters per second to kilometers per hour, we multiply by 18/5:
v1 = 11.8 × 18/5
v1 = 42.48 km/hr
Therefore, the speed of the faster train is approximately 42.48 km/hr, which is closest to option A (46.8 km/hr).
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Two trains, whose respective lengths are 120 metres and 180 metres, cross each other in 15 seconds when they are moving in opposite directions and in 50 seconds when they are moving in the same direction. What is the speed of the faster train (in km/hr)?a)46.8 kmphb)40.2 kmphc)54 kmphd)56.5 kmphe)None of theseCorrect answer is option 'A'. Can you explain this answer?
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Two trains, whose respective lengths are 120 metres and 180 metres, cross each other in 15 seconds when they are moving in opposite directions and in 50 seconds when they are moving in the same direction. What is the speed of the faster train (in km/hr)?a)46.8 kmphb)40.2 kmphc)54 kmphd)56.5 kmphe)None of theseCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Two trains, whose respective lengths are 120 metres and 180 metres, cross each other in 15 seconds when they are moving in opposite directions and in 50 seconds when they are moving in the same direction. What is the speed of the faster train (in km/hr)?a)46.8 kmphb)40.2 kmphc)54 kmphd)56.5 kmphe)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two trains, whose respective lengths are 120 metres and 180 metres, cross each other in 15 seconds when they are moving in opposite directions and in 50 seconds when they are moving in the same direction. What is the speed of the faster train (in km/hr)?a)46.8 kmphb)40.2 kmphc)54 kmphd)56.5 kmphe)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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