Q:- The sum of the digit …

Let the ten’s and the unit’s digits in the first number be x and y, respectively.

So, the first number may be written as 10 x + y in the expanded form (for example, 56 = 10(5) + 6).

When the digits are reversed, x becomes the unit’s digit and y becomes the ten’s digit.

This number, in the expanded notation is 10y + x (for example, when 56 is reversed, we get 65 = 10(6) + 5).

According to the given condition. (10x + y) + (10y + x) = 66 i.e., 11(x + y) = 66 i.e., x + y = 6  ..... (1)

We are also given that the digits differ by 2, therefore, either x – y = 2   ........(2) or y – x = 2   ..........(3)

If x – y = 2, then solving (1) and (2) by elimination, we get x = 4 and y = 2.

In this case, we get the number 42. If y – x = 2, then solving (1) and (3) by elimination, we get x = 2 and y = 4.

In this case, we get the number 24. Thus, there are two such numbers 42 and 24.