Multiple choice

A train travelling at $36$ km/hr passes in $12$ seconds another train half its length travelling in the opposite direction at $54$ km/hr, If it also passes a railway platform in $\displaystyle 1\frac{1}{2}$ minutes what is the length of the platform?

  1. $800$ m
  2. $700$ m
  3. $900$ m
  4. $1000$ m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train 1 speed = 10 m/s, Train 2 speed = 15 m/s. Relative speed = 25 m/s. Length L1 + L2 = 25 * 12 = 300. Since L2 = L1/2, 1.5*L1 = 300, so L1 = 200 and L2 = 100. Passing platform in 90s: (L1 + L_platform) = 10 * 90 = 900. L_platform = 900 - 200 = 700.

AI explanation

Convert the speeds to meters per second to get 10 m/s for the first train and 15 m/s for the second train. Let the length of the first train be L, so the second train's length is L/2; the total distance covered when passing is L plus L/2, which is 1.5L. Using the relative speed for opposite directions, which is 10 plus 15 equals 25 m/s, the equation is 1.5L equals 25 times 12 seconds, solving to a first train length of 200 meters. To find the platform length, convert 1.5 minutes to 90 seconds, so the distance covered is 10 m/s times 90 seconds, totaling 900 meters; subtracting the train's 200 meter length leaves a platform length of 700 meters.

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