Question

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 reverse pairs?
1. 94
2. 320
3. 188
4. 210
5. 150

Answer 1

Correct Answer - Option 4 : 210

Given:

Ratio of two digit number formed by reversing its digits = 4 : 7

Assumption:

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

Calculation:

(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

b     a        Number   Reverse

2     1             12          21

4     2             24          42

6     3             36          63

8     4             48          84

Reverse pair: 21 + 42 + 63 + 84 = 210