Multiple choice

A train crosses a platform in 27 seconds with a speed of 36 km/hour and takes 18 seconds to cross a man running in the same direction with a speed of 9 km/hour. What is the length of the platform?

  1. 112 m

  2. 126 m

  3. 135 m

  4. 145 m

  5. 158 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed of train = 36 km/h = 10 m/s. Speed of man = 9 km/h = 2.5 m/s. Relative speed (same direction) = 10 - 2.5 = 7.5 m/s. Length of train = 7.5 m/s * 18 s = 135 m. Time to cross platform = 27 s, so total distance = 10 m/s * 27 s = 270 m. Length of platform = 270 - 135 = 135 m.

AI explanation

The speed of the train is 36 km/hr, which converts to 36 multiplied by (5 divided by 18), equaling 10 m/s. When crossing the platform, the total distance covered is 10 multiplied by 27, which equals 270 metres. When crossing the man running in the same direction, the relative speed is (36 minus 9) km/hr, equaling 27 km/hr or 7.5 m/s; therefore, the train's length is 7.5 multiplied by 18, equaling 135 metres. Subtracting this train length from the total distance gives the platform length of 270 minus 135, equaling 135 metres.

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