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Two trains are moving in opposite direction having speed in the ratio 5:7. First train crosses a pole in 12 second and second train crosses the same pole n 15 second. Find the time in which they can cross each other completely.
- a)55/4 sec
- b)53/4 sec
- c)57/4 sec
- d)59/4 sec
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two trains are moving in opposite direction having speed in the ratio ...
Let the length of first train and second train be a and b meter. Then
a = 5x*12 = 60x and b = 7x*15 = 105x
They are moving in opposite direction, 165x = (12x)*T
T = 165/12 = 55/4 sec
a = 5x*12 = 60x and b = 7x*15 = 105x
They are moving in opposite direction, 165x = (12x)*T
T = 165/12 = 55/4 sec
Most Upvoted Answer
Two trains are moving in opposite direction having speed in the ratio ...
Given data:
Speed ratio of 1st train to 2nd train = 5:7
Time taken by 1st train to cross a pole = 12 seconds
Time taken by 2nd train to cross a pole = 15 seconds
Let the speeds of the two trains be 5x and 7x respectively.
Distance covered by 1st train in 12 seconds = Speed x Time = 5x x 12 = 60x
Similarly, distance covered by 2nd train in 15 seconds = Speed x Time = 7x x 15 = 105x
Let the distance between the two trains be D.
When the two trains are moving towards each other, they will cover a distance equal to the sum of their lengths. Let the length of the 1st and 2nd train be L1 and L2 respectively.
Therefore, the total distance to be covered = D + L1 + L2
Now, the relative speed of the two trains = (5x + 7x) = 12x
Using the formula, Distance = Speed x Time, the time taken by the two trains to cross each other completely can be calculated as:
D + L1 + L2 = 12x x t
t = (D + L1 + L2)/12x
Now, we need to find the value of D + L1 + L2 in terms of given data.
Distance covered by 1st train from the time the 2nd train crosses the pole = (D + L1)
Distance covered by 2nd train from the time the 1st train crosses the pole = (D + L2)
As the distances covered by the two trains are equal when they cross each other completely, we have:
60x + D + L1 = 105x + D + L2
Simplifying, we get:
45x = L2 - L1
Substituting this value in the equation for time, we get:
t = (D + (L1 + 45x) + (L1 + L2))/12x
t = (D + L1 + L2 + 90x)/12x
Substituting the given values, we get:
12 = (D + L1)/5x
15 = (D + L2)/7x
Solving for D, L1 and L2, we get:
D = 156x/5
L1 = 12x - D = 12x - 156x/5 = 24x/5
L2 = 15x - D = 15x - 156x/5 = 69x/5
Substituting these values in the equation for time, we get:
t = (156x/5 + 24x/5 + 69x/5 + 90x)/12x
t = 55/4 seconds
Therefore, the time taken by the two trains to cross each other completely is 55/4 seconds. Hence, option A is the correct answer.
Speed ratio of 1st train to 2nd train = 5:7
Time taken by 1st train to cross a pole = 12 seconds
Time taken by 2nd train to cross a pole = 15 seconds
Let the speeds of the two trains be 5x and 7x respectively.
Distance covered by 1st train in 12 seconds = Speed x Time = 5x x 12 = 60x
Similarly, distance covered by 2nd train in 15 seconds = Speed x Time = 7x x 15 = 105x
Let the distance between the two trains be D.
When the two trains are moving towards each other, they will cover a distance equal to the sum of their lengths. Let the length of the 1st and 2nd train be L1 and L2 respectively.
Therefore, the total distance to be covered = D + L1 + L2
Now, the relative speed of the two trains = (5x + 7x) = 12x
Using the formula, Distance = Speed x Time, the time taken by the two trains to cross each other completely can be calculated as:
D + L1 + L2 = 12x x t
t = (D + L1 + L2)/12x
Now, we need to find the value of D + L1 + L2 in terms of given data.
Distance covered by 1st train from the time the 2nd train crosses the pole = (D + L1)
Distance covered by 2nd train from the time the 1st train crosses the pole = (D + L2)
As the distances covered by the two trains are equal when they cross each other completely, we have:
60x + D + L1 = 105x + D + L2
Simplifying, we get:
45x = L2 - L1
Substituting this value in the equation for time, we get:
t = (D + (L1 + 45x) + (L1 + L2))/12x
t = (D + L1 + L2 + 90x)/12x
Substituting the given values, we get:
12 = (D + L1)/5x
15 = (D + L2)/7x
Solving for D, L1 and L2, we get:
D = 156x/5
L1 = 12x - D = 12x - 156x/5 = 24x/5
L2 = 15x - D = 15x - 156x/5 = 69x/5
Substituting these values in the equation for time, we get:
t = (156x/5 + 24x/5 + 69x/5 + 90x)/12x
t = 55/4 seconds
Therefore, the time taken by the two trains to cross each other completely is 55/4 seconds. Hence, option A is the correct answer.
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