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Question 6 : The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

  1. 30
  2. 28
  3. 32
  4. 26

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Explanatory Answer

Method of solving this CAT Question from Averages
CAT 2017 Question Paper Quants Slot 2 Averages

From the given data let us assume the average height of 22 toddlers to be a
If two of them leaves this group then average height of 20 toddlers increases by 2 so a + 2
If the average height of two toddlers who leaves the group is one third the average height of the original 22
No.of toddlers × average = Total
Hence we can write the equation in such a way that,
22a = 20(a + 2) + \\frac{2a}{3})
2a – \\frac{2a}{3}) = 40
⟹ \\frac{4a}{3}) = 40
a = 30
We need to find the average of remaining 20 toddlers.
⟹ a + 2 = 30 + 2 = 32

The question is "The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is"

Hence, the answer is 32

Choice C is the correct answer

 

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