# CAT Practice : Averages, Ratios, Mixtures

A ratio proportion question that involves using a simple framework from number systems.

## Ratios - Number Systems

Q.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

Choice C. 330

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## Detailed Solution

Let the two digit number be 10a + b and the number formed by reversing its digits be 10b + a.

10a + b / 10b + a
=
4 / 7

70a + 7b = 40b + 4a
66a = 33b
Therefore,
a / b
=
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.

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