A good train and a passenger train are running on parallel tracks in the same…
2023
A good train and a passenger train are running on parallel tracks in the same direction . The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec . Whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec . If the speeds of the trains be in the ratio 1:2 . Find the ratio of their lengths .
- A.
3:1
- B.
2:1
- C.
3;2
- D.
4:3
Attempted by 3 students.
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Correct answer: B
Let the speed of the goods train be s and the speed of the passenger train be 2s. Let the lengths of the goods and passenger trains be L_g and L_p respectively.
Relative speed (passenger relative to goods) = 2s - s = s.
Observation by the driver of the goods train: The passenger train overtakes and crosses the goods train completely in 60 s. The distance covered relative to the goods train during this event is the sum of the two lengths, so (L_g + L_p)/s = 60, hence L_g + L_p = 60s.
Observation by a passenger on the passenger train: If the passenger measures the time his train takes to pass a fixed point on the goods train (for example the goods-driver's position), that time equals the passenger train's length divided by the relative speed, so L_p/s = 40, hence L_p = 40s.
Substitute L_p = 40s into L_g + L_p = 60s to get L_g = 20s.
Therefore the ratio of lengths (passenger : goods) is L_p : L_g = 40s : 20s = 2 : 1.
Answer: 2:1.