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Trains and Platform Length

CMAT 2024 · Quantitative Techniques & Data Interpretation · Medium · Speed, Distance and Time

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A train travelling at 48 km/h completely crosses another train having half the length of first train and travelling in opposite direction at 42 km/h in 12 seconds. The train having speed 48 km/h also passes a railway platform in 45 seconds. What is the length of the platform ?

  1. A.

    600 m

  2. B.

    300 m

  3. C.

    400 m

  4. D.

    200 m

Answer

C

Explanation

Let length of 1st train be xx m. Length of 2nd train = 0.5x0.5x m. Relative speed = 48+42=9048 + 42 = 90 km/h = 90×518=2590 \times \frac{5}{18} = 25 m/s. Distance covered = x+0.5x=1.5xx + 0.5x = 1.5x. 1.5x=25×12=300  ⟹  x=2001.5x = 25 \times 12 = 300 \implies x = 200 m.

Now, speed of 1st train = 4848 km/h = 48×518=40348 \times \frac{5}{18} = \frac{40}{3} m/s. Passing platform of length LL in 45 s: 200+L40/3=45  ⟹  200+L=45×403=600  ⟹  L=400\frac{200 + L}{40/3} = 45 \implies 200 + L = 45 \times \frac{40}{3} = 600 \implies L = 400 m.

Hence, Option C is correct.

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