A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is

Step 1: Let's denote the two-digit number as 10x + y, where x and y are the tens and units digits respectively.

Step 2: According to the problem, the product of the digits is 8. So, we have the equation: xy = 8.

Step 3: It is also given that when 18 is added to the number, the digits are reversed. This means that 10x + y + 18 = 10y + x.

Step 4: Simplify the above equation to get: 9x + 18 = 9y. Divide the entire equation by 9 to get: x + 2 = y.

Step 5: Now we have two equations: xy = 8 and x + 2 = y. We can solve these equations simultaneously to find the values of x and y.

Step 6: Substitute y in the first equation with x + 2 to get: x(x + 2) = 8. This simplifies to: x^2 + 2x - 8 = 0.

Step 7: Solve this quadratic equation to get the possible values of x. The solutions are x = 2 and x = -4. Since x represents a digit, it cannot be negative. So, x = 2.

Step 8: Substitute x = 2 in the equation x + 2 = y to get y = 4.

Step 9: Therefore, the two-digit number is 24.