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Two trains of lengths in the ratio of 1 : 2, running in opposite directions, pass a pole in 12 and 8 seconds. The trains will cross each other in
- a)9 seconds
- b)15 seconds
- c)18 seconds
- d)20 seconds
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two trains of lengths in the ratio of 1 : 2, running in opposite direc...
Let to length of trains be L and 2L respectively,
Speed of the trains be S1 and S2 respectively,
We know that, when a train passes a pole, it travels a distance equal to its own length.
First train passes the pole in 12 seconds.
∴ S1 = L/12
Second train passes the pole in 8 seconds.
S2 = 2L/8 = L/4
According to the given information, they are running in opposite directions,
Thus ,
Relative Speed (S)
When two trains cross each other, each of them travels a distance equal to sum of their lengths.
∴ Distance to be traveled = L + 2L = 3L
Time taken to cross each other
Speed of the trains be S1 and S2 respectively,
We know that, when a train passes a pole, it travels a distance equal to its own length.
First train passes the pole in 12 seconds.
∴ S1 = L/12
Second train passes the pole in 8 seconds.
S2 = 2L/8 = L/4
According to the given information, they are running in opposite directions,
Thus ,
Relative Speed (S)
When two trains cross each other, each of them travels a distance equal to sum of their lengths.
∴ Distance to be traveled = L + 2L = 3L
Time taken to cross each other
Most Upvoted Answer
Two trains of lengths in the ratio of 1 : 2, running in opposite direc...
Understanding the Problem
To solve this problem, we have two trains with lengths in the ratio of 1:2. Let's denote the length of the first train as L and the second train as 2L.
Pass Time at a Pole
- The first train passes a pole in 12 seconds.
- The second train passes a pole in 8 seconds.
Calculating Speeds
- Speed of the first train = Length / Time = L / 12
- Speed of the second train = Length / Time = 2L / 8 = L / 4
Combined Speed
When two trains move in opposite directions, their speeds add up:
- Combined speed = (L / 12) + (L / 4)
- To add these fractions, find a common denominator (which is 12):
- L / 12 + 3L / 12 = 4L / 12 = L / 3
Finding the Total Length
The total length of the two trains is:
- Total length = L + 2L = 3L
Time to Cross Each Other
Now, to find the time taken to cross each other:
- Time = Total Length / Combined Speed
- Time = (3L) / (L / 3)
- Time = 3L * (3 / L) = 9 seconds
Conclusion
Thus, the trains will cross each other in 9 seconds, which confirms that option 'A' is correct.
To solve this problem, we have two trains with lengths in the ratio of 1:2. Let's denote the length of the first train as L and the second train as 2L.
Pass Time at a Pole
- The first train passes a pole in 12 seconds.
- The second train passes a pole in 8 seconds.
Calculating Speeds
- Speed of the first train = Length / Time = L / 12
- Speed of the second train = Length / Time = 2L / 8 = L / 4
Combined Speed
When two trains move in opposite directions, their speeds add up:
- Combined speed = (L / 12) + (L / 4)
- To add these fractions, find a common denominator (which is 12):
- L / 12 + 3L / 12 = 4L / 12 = L / 3
Finding the Total Length
The total length of the two trains is:
- Total length = L + 2L = 3L
Time to Cross Each Other
Now, to find the time taken to cross each other:
- Time = Total Length / Combined Speed
- Time = (3L) / (L / 3)
- Time = 3L * (3 / L) = 9 seconds
Conclusion
Thus, the trains will cross each other in 9 seconds, which confirms that option 'A' is correct.
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Two trains of lengths in the ratio of 1 : 2, running in opposite directions, pass a pole in 12 and 8 seconds. The trains will cross each other ina)9 secondsb)15 secondsc)18 secondsd)20 secondsCorrect answer is option 'A'. Can you explain this answer?
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