Multiple choice

The length of a train and that of a platform are equal. If with the speed of $54$ km/hr, the train crosses the platform in 1$\displaystyle \frac{1}{2}$ minutes, then what is the length of the platform in metres?

  1. $675$ m
  2. $505$ m
  3. $847$ m
  4. $620$ m
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A Correct answer
Explanation

Speed = 54 km/hr = 54 * (5/18) = 15 m/s. Time = 1.5 minutes = 90 seconds. Total distance = Speed * Time = 15 * 90 = 1350 m. Since train length = platform length, 2 * platform = 1350, so platform = 675 m.

AI explanation

Using the conversion formula, a speed of 54 km/hr equals 54 multiplied by 5/18, which is 15 m/s. The total distance covered to cross the platform is the sum of the lengths of the train and the platform, so it is 2L. The time taken is 1.5 minutes, which is 90 seconds, so 2L equals 15 m/s multiplied by 90 seconds, giving a total distance of 1350 m. Therefore, the length of the platform L is 1350 divided by 2, which is 675 m. The result is 675 m.

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