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:

Let the ten's and unit digit be x and $$\frac{8}{x}$$ respectively
$$\eqalign{ & {\text{Then,}} \cr & \left( {10x + \frac{8}{x}} \right) + 18 = 10 \times \frac{8}{x} + x \cr & \Rightarrow 10{x^2} + 8 + 18x = 80 + {x^2} \cr & \Rightarrow 9{x^2} + 18x - 72 = 0 \cr & \Rightarrow {x^2} + 2x - 8 = 0 \cr & \Rightarrow \left( {x + 4} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2 \cr} $$
∴ first digit will be 2 and second digit will be 4.
i.e digit is 24.