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GATE 2018 ME (ME1) – Question 8

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

At constant speed 54 km/h, 25 seconds elapse between a train’s front entering and rear leaving a platform. At the same speed it passes a man running at 9 km/h in its direction in 14 seconds. Train and platform lengths respectively are ______.

  1. 210 m and 140 m
  2. 162.5 m and 187.5 m
  3. 245 m and 130 m
  4. 175 m and 200 m

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Show answer and explanation

Correct answer: (D) 175 m and 200 m

Explanation

Train speed is 15 m/s; relative speed past the runner is $15-2.5=12.5$ m/s. Train length is $12.5(14)=175$ m. Train plus platform length is $15(25)=375$ m, leaving platform length 200 m (D).