Multiple choice

Find the value of quantities and state the correct relationship.\newline Quantity I: The length of the train if train crosses a pole in 30 sec and a platform of 300 m length in 60 seconds.\newline Quantity II: The length of a platform if 200 m long train crosses a pole in 25 sec and platform in 55 sec

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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A Correct answer
Explanation

Quantity I: Train speed = v. Crossing pole (length L) in 30s: v = L/30. Crossing 300m platform in 60s: (L+300)/v = 60. Substituting v gives (L+300)/(L/30) = 60, so L+300 = 2L, hence L = 300m. Quantity II: Train speed = v = 200/25 = 8 m/s. Crossing platform in 55s: (200+P)/8 = 55, so 200+P = 440, hence P = 240m. Comparing: 300 > 240, so Quantity I > Quantity II.

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