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The question is from CAT Ratio, Mixtures and Averages. This combines number theory with ratio. We need to find the sum of all possible numbers that satisfy the given condition. 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 3: The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

  1. 99
  2. 198
  3. 330
  4. 132

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Explanatory Answer

Method of solving this CAT Question from Ratio, Mixtures and Averages: A ratio proportion question that involves using a simple framework from number systems.

Let the two digit number be 10a + b and the number formed by reversing its digits be 10b + a.
\\frac{10a + b}{10b + a}\\) = \\frac{4}{7}\\)
70a + 7b = 40b + 4a
66a = 33b
Therefore, \\frac{a}{b}\\) = \\frac{1}{2}\\)

So, let us list down all possible values for a and b.

a b Number Reversed Number
1 2 12 21
2 4 24 42
3 6 36 63
4 8 48 84

Hence, the sum of all the numbers would be,
12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330.

The question is "Which of the following is the sum of all the numbers of all such pairs?"

Hence, the answer is "330".

Choice C is the correct answer.

 

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