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The question is from CAT Ratio, Mixtures and Averages. When we find the average of the speed, we don't use simple arithmetic mean. Why we can't use that? CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019.

Question 39: Ram travels half of his journey by train at 80 kmph, half of the remaining with bus at 40 kmph and the rest with cycle at 20 kmph. Find his average speed during the entire journey.

  1. 33.33 kmph
  2. 40 kmph
  3. 50 kmph
  4. 45 kmph

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Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: Why do we use harmonic mean here?

Let the distance travelled be d.

Average Speed = \\frac{Total Distance Travelled}{Total time taken}\\)

=\\frac{d}{\frac{d}{2}*80}\\) + \\frac{d}{4*40}\\) + \\frac{d}{4*20}\\) = \\frac{1}{(1+1+2)/160}\\) = \\frac{160}{4}\\) = 40 Kmph

The question is "Find his average speed during the entire journey."

Hence, the answer is "40 kmph".

Choice D is the correct answer.

 


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