The sum of a two digit number and the number obtained by reversing the digits is 66.If the digits of the number differ by 2, find the number. How many such numbers arethere?

Sure, let's solve this step by step.

Step 1: Let's denote the tens digit as 'x' and the units digit as 'y'. So, the two-digit number can be represented as 10x + y.

Step 2: The number obtained by reversing the digits is 10y + x.

Step 3: According to the problem, the sum of the original number and the reversed number is 66. So, we can write the equation as (10x + y) + (10y + x) = 66. Simplifying this equation, we get 11x + 11y = 66, or x + y = 6.

Step 4: The problem also states that the digits of the number differ by 2. So, we can write another equation as |x - y| = 2.

Step 5: Now, we have a system of two equations: x + y = 6 and |x - y| = 2. Solving this system, we get two pairs of solutions: (x, y) = (4, 2) and (x, y) = (2, 4).

Step 6: Therefore, the two numbers that satisfy the conditions of the problem are 42 and 24. So, there are 2 such numbers.