CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

CAT Questions | Speed Time | Relative Speed

The question is from the topic of Relative Speed. This is a classic CAT level question testing your understanding in the concept of relative speed from Time Speed and Distance. Time Speed and Distance is a favorite in CAT Exam and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 26: Two trains A and B are 100 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.

  1. 10 s
  2. 6 s
  3. 4 s
  4. 8 s

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Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Finding the relative speed of the trains will give head start.

Speed of A = 54 * \\frac{1000}{60*60}\\) = 15 m/s
Speed of B = 36 * \\frac{1000}{60*60}\\) = 10 m/s

Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m.
Therefore time taken = \\frac{150}{25}\\) = 6s
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 100 + 150 = 250 m. Time taken = \\frac{250}{25}\\) = 10 s

The question is " Calculate the time taken by Arun to completely cross Train B. "

Hence, the answer is 6 s.

Choice B is the correct answer.


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