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A train passes two persons walking in opposite directions to the train at a speed of 5 m/s and 10 m/s  and crosses them in 6 seconds and 5 seconds respectively. Find the length of the train?

  • a)
    140 m

  • b)
    150 m

  • c)
    160 m

  • d)
    120 m

Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A train passes two persons walking in opposite directions to the train...
Let the speed of the train be 's' m/s.


Let the length of the train be 'x' meters.


Relative speed of train and the first person who is moving at the speed of 5 m/s in opposite direction = (s+5) m/s.


Therefore, total distance travelled (i.e length of train) 'x'= Relative speed X time


x = (s+5) * 6 …. ( Eq 1)


Relative speed of train and the second person who is moving at the speed of 10 m/s in opposite direction = (s+10) m/s


Therefore, total distance travelled (i.e length of train) 'x' = Relative speed X time


x = (s+10) * 5 …. (Eq 2)


Since length of the train is same in both the cases, if we equate the equation 1 and equation 2 we get


⇒ (s+5) * 6 = (s+10) * 5


⇒ 6s+30= 5s+50


⇒ 6s - 5s = 50 - 30


⇒ s = 20 m/s (i.e speed of the train)


Now, putting the value of speed of the train in equation 1 (we can put the value equation 2 as well) we get


Length of the train 'x' = (20+5) * 6




  • x = 25 * 6



  • x= 150




Therefore, length of the train is 150 meters.
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Most Upvoted Answer
A train passes two persons walking in opposite directions to the train...
Given data:
- Speed of the train relative to the first person = 5 m/s
- Speed of the train relative to the second person = 10 m/s
- Time taken to pass the first person = 6 seconds
- Time taken to pass the second person = 5 seconds

Let's assume the length of the train to be 'L' meters.

Formula used:
- Relative speed = Speed of the train - Speed of the person (when walking in opposite directions)

Calculation:
- Let the distance covered by the train in 6 seconds be 'D1' meters.
- D1 = Relative speed × Time taken to pass the first person
- D1 = (5 + x) × 6, where 'x' is the speed at which the first person is walking.
- Let the distance covered by the train in 5 seconds be 'D2' meters.
- D2 = Relative speed × Time taken to pass the second person
- D2 = (10 + x) × 5
- Equating D1 and D2, we get:
- (5 + x) × 6 = (10 + x) × 5
- Solving this equation, we get x = 15 m/s
- Therefore, the length of the train, L = Relative speed × Time taken to cross the first person
- L = (5 + 15) × 6 = 120 meters

Therefore, the correct answer is option B, i.e., 150 m.
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A train passes two persons walking in opposite directions to the train at a speed of 5 m/s and 10 m/s and crosses them in 6 seconds and 5 seconds respectively. Find the length of the train?a)140 mb)150 mc)160 md)120 mCorrect answer is option 'B'. Can you explain this answer?
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