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    Question

    Train X passes a pole in 18 seconds and a platform of

    length 300 m in 30 seconds. Another train Y passes a pole in 12 seconds. When the two trains run in opposite directions, they completely cross each other in 16 seconds. Find: (i) The length of each train (ii) The speed of train Y in km/h. Choose the correct options:- A) (i) Lengths: Train X = 400 m; Train Y = 150 m. (ii) Speed of train Y = 45 km/h. B) (i) Lengths: Train X = 250 m; Train Y = 100 m. (ii) Speed of train Y = 15 km/h. C) (i) Lengths: Train X = 350 m; Train Y = 100 m. (ii) Speed of train Y = 35 km/h. D) (i) Lengths: Train X = 450 m; Train Y = 150 m. (ii) Speed of train Y = 45 km/h. E) None of these
    A A Correct Answer Incorrect Answer
    B B Correct Answer Incorrect Answer
    C C Correct Answer Incorrect Answer
    D D Correct Answer Incorrect Answer
    E E Correct Answer Incorrect Answer

    Solution

    ATQ, Let length of train X = Lx metres, speed = Sx m/s. From “passes a pole in 18 s”: Lx / Sx = 18 ⇒ Lx = 18 Sx. From “passes 300 m platform in 30 s”: (Lx + 300) / Sx = 30 ⇒ (18Sx + 300)/Sx = 30 ⇒ 18 + 300/Sx = 30 ⇒ 300/Sx = 12 ⇒ Sx = 25 m/s. Then Lx = 18 × 25 = 450 m. Train Y: Let length Ly (m), speed Sy (m/s). From “passes a pole in 12 s”: Ly / Sy = 12 ⇒ Ly = 12 Sy. When crossing each other in opposite directions in 16 s: (Lx + Ly) / (Sx + Sy) = 16 Substitute Lx, Ly, Sx: (450 + 12Sy) / (25 + Sy) = 16 ⇒ 450 + 12Sy = 16(25 + Sy) ⇒ 450 + 12Sy = 400 + 16Sy ⇒ 12Sy − 16Sy = 400 − 450 ⇒ −4Sy = −50 ⇒ Sy = 12.5 m/s. Then Ly = 12 × 12.5 = 150 m. Convert Sy to km/h: 1 m/s = 3.6 km/h ⇒ Sy = 12.5 × 3.6 = 45 km/h. Answer: (i) Lengths: Train X = 450 m; Train Y = 150 m. (ii) Speed of train Y = 45 km/h.

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