The document describes a ratio problem involving two-digit numbers and their reversals. It shows that the only possible pairs are: 1) 12 and 21 2) 24 and 42 3) 36 and 63 4) 48 and 84 The sum of all the numbers in these pairs is 330. Therefore, the answer is c.

1. Ratio Proportion

2. Ratio Proportion
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?
(a) 99 (b) 198
(c) 330 (d) 132

3. Ratio Proportion
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
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?

4. Ratio Proportion
So, let us list down all possible values for a and b.
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?
a b Number Reversed Number
1 2 12 21
2 4 24 42
3 6 36 63
4 8 48 84

5. Ratio Proportion
Hence, the sum of all the numbers would be,
12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330.
Answer choice (c)
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?

6. For lots more CAT Level Questions, visit
online.2iim.com