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A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in the opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train?
- a)2 : 1
- b)3 : 2
- c)4 : 3
- d)1 : 1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A passenger train and a goods train are running in the same direction ...
For crossing the relative displacement is same and equal to the sum lengths of the trains in both cases
∴ Time ∝ 1/Relative speed
Let the speed of the goods train be x and passenger train be kx, where k is required ratio
Relative speed when moving in opposite direction = kx - (-x) = (k + 1)x [Speeds are added]
Relative speed when moving in same direction = kx - x = (k - 1)x
(Time taken when moving in same direction) / (Time taken when moving in opposite direction) = (Relative Speed in opposite direction) / (Relative Speed in same direction)
3 = (k + 1)x / [(k - 1)x]
3 = (k + 1) / (k - 1)
3k - 3 = k + 1
2k = 4
k = 2
∴ The required ratio = 2 : 1
3 = (k + 1) / (k - 1)
3k - 3 = k + 1
2k = 4
k = 2
∴ The required ratio = 2 : 1
Most Upvoted Answer
A passenger train and a goods train are running in the same direction ...
Given:
Passenger train and a goods train are running in the same direction on parallel railway tracks.
To Find:
Ratio of the speed of the passenger train to that of the goods train.
Solution:
Let the length of the passenger train be P and the length of the goods train be G.
Let the speed of the passenger train be p and the speed of the goods train be g.
When they are running in the same direction,
Relative speed = p - g
Time taken to cross the goods train = (P + G) / (p-g)
When they are running in opposite directions,
Relative speed = p + g
Time taken to cross the goods train = (P + G) / (p+g)
Given that the time taken to cross the goods train when they are running in the same direction is three times the time taken when they are running in opposite directions.
(P + G) / (p-g) = 3(P + G) / (p+g)
p/g = 2/1
Therefore, the ratio of the speed of the passenger train to that of the goods train is 2:1
Answer: Option A (2:1)
Passenger train and a goods train are running in the same direction on parallel railway tracks.
To Find:
Ratio of the speed of the passenger train to that of the goods train.
Solution:
Let the length of the passenger train be P and the length of the goods train be G.
Let the speed of the passenger train be p and the speed of the goods train be g.
When they are running in the same direction,
Relative speed = p - g
Time taken to cross the goods train = (P + G) / (p-g)
When they are running in opposite directions,
Relative speed = p + g
Time taken to cross the goods train = (P + G) / (p+g)
Given that the time taken to cross the goods train when they are running in the same direction is three times the time taken when they are running in opposite directions.
(P + G) / (p-g) = 3(P + G) / (p+g)
p/g = 2/1
Therefore, the ratio of the speed of the passenger train to that of the goods train is 2:1
Answer: Option A (2:1)
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A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in the opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train?a)2 : 1b)3 : 2c)4 : 3d)1 : 1Correct answer is option 'A'. Can you explain this answer?
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