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A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
- a)200 m
- b)500 m
- c)100 m
- d)300 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A train overtakes two persons who are walking at the rate of 8 kmph an...
8 kmph = (8 x 5/18) = 20/9 m/sec
4 kmph = (12 x 5/18 = 10/3 m/sec
18 9
Let the length of the train be x metres and its speed by y m/sec.
Then, [x/(y - 20/9)] = 9 and [x/(y - 10/3)] = 10
Therefore 9y - 20 = x and 10y - 100/3 = x
=> 9y - 20 = 10y - 100/3
solving: y = 40/3
putting value of y in (1):
9 . (40/3) - 20 = x
so, x = 100 m
On solving, we get: x = 100.
Therefore Length of the train is 100 m.
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A train overtakes two persons who are walking at the rate of 8 kmph an...
Given data:
Speed of first person = 8 kmph
Speed of second person = 12 kmph
Time taken by the train to pass the first person completely = 9 seconds
Time taken by the train to pass the second person completely = 10 seconds
To find:
Length of the train
Solution:
Let the length of the train be ‘x’ meters
Speed of the train = relative speed of train with respect to the person
When the train overtakes the first person:
Relative speed = Speed of train - Speed of person
= (x/9 - 8) kmph
When the train overtakes the second person:
Relative speed = Speed of train - Speed of person
= (x/10 - 12) kmph
As the train covers its own length in both cases, we can equate the distances covered by the train in both cases.
Therefore, x = (x/9 - 8) × 9 = (x/10 - 12) × 10
9x = (x - 72) × 9 × 10
9x = 90x - 720
81x = 720
x = 8.88 ≈ 9 (Approximately)
Therefore, the length of the train is 9 meters.
Answer: Option (d) 300 m
Speed of first person = 8 kmph
Speed of second person = 12 kmph
Time taken by the train to pass the first person completely = 9 seconds
Time taken by the train to pass the second person completely = 10 seconds
To find:
Length of the train
Solution:
Let the length of the train be ‘x’ meters
Speed of the train = relative speed of train with respect to the person
When the train overtakes the first person:
Relative speed = Speed of train - Speed of person
= (x/9 - 8) kmph
When the train overtakes the second person:
Relative speed = Speed of train - Speed of person
= (x/10 - 12) kmph
As the train covers its own length in both cases, we can equate the distances covered by the train in both cases.
Therefore, x = (x/9 - 8) × 9 = (x/10 - 12) × 10
9x = (x - 72) × 9 × 10
9x = 90x - 720
81x = 720
x = 8.88 ≈ 9 (Approximately)
Therefore, the length of the train is 9 meters.
Answer: Option (d) 300 m
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A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?a)200 mb)500 mc)100 md)300 mCorrect answer is option 'C'. Can you explain this answer?
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