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The question is from CAT Ratio, Mixtures and Averages. We need to determine the number of students from the given details about the average. 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 21: A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got! How many students were there in the class?

  1. 30
  2. 26
  3. 11
  4. 31

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Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: We need to find out the share of the other students first! Their share plus 1/6th is total share, from which we can find the total number of students...

Let the total students be (n + 1)
Let total badges be x
Let the average of ‘n’ students be y
The student who got \\frac{1}{6}\\)th of x = 5y
Or y = \\frac{x}{30}\\)
Therefore ‘n’ students got \\frac{1}{30}\\)th of total share each
Or n * \\frac{x}{30}\\)+ 1 * \\frac{x}{6}\\) = x
nx + 5x = 30x
n + 5 = 30
Or n = 25
Total = n + 1 = 26

The question is "How many students were there in the class?"

Hence, the answer is "26".

Choice B is the correct answer.


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