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Trains P and Q are moving on parallel tracks in the same direction. Train P crosses train Q completely in 60 seconds and a passenger in train P crosses train Q in 40 seconds. If the speeds of trains…

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Trains P and Q are moving on parallel tracks in the same direction. Train P crosses train Q completely in 60 seconds and a passenger in train P crosses train Q in 40 seconds. If the speeds of trains P and Q are in the ratio 2 : 1, then calculate the ratio of their lengths (P : Q)?
  1. 3 : 4
  2. 1 : 2
  3. 3 : 1
  4. 3 : 2

Answer and explanation

Correct answer: B - 1 : 2
The speeds are 2v2v and vv, so the relative speed is vv. A passenger on P passes Q's whole length in 40 s, so LQ=40vL_Q = 40v. P passes Q completely in 60 s, so LP+LQ=60vL_P + L_Q = 60v and LP=20vL_P = 20v. LP:LQ=1:2L_P : L_Q = 1 : 2.

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