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:

Answer: Option B

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