A train takes 36 seconds to pass a man walking at 2 m/s in the same direction and 48 seconds to cross a platform whose length is 50% more than the train. A 60-metre-long tractor is coming from the opposite direction at 6 m/s. Find the time taken by the train to completely cross the tractor. (in approx.)
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Correct answer: B
Explanation
Given:
Speed of the person = 2 m/s
Train passes the person = 36 s
Time to cross the platform = 48 s
Length of the platform = 50% more than the length of the train
Length of the tractor = 60 m
Speed of the tractor = 6 m/s (opposite direction)
Let the speed of the train = v m/s
Length of the train = L
Relative speed while passing the person = v − 2
L = (v − 2) × 36 ...(1)
Length of the platform = 1.5L
Total distance = L + 1.5L = 2.5L
2.5L = v × 48
L = 19.2v ...(2)
From (1) and (2),
36(v − 2) = 19.2v
36v − 72 = 19.2v
16.8v = 72
v = 4.2857 m/s
L = 19.2 × 4.2857 = 82.29 m
Total distance with tractor = 82.29 + 60 = 142.29 m
Relative speed= 4.2857 + 6= 10.2857 m/s
Time = 142.29 ÷ 10.2857 = 14 seconds