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's digits be $$x$$ and $$\frac{8}{x}$$ respectively
Then,
$$\begin{array}{rl}& \iff \left(10x+\frac{8}{x}\right)+18=10\times \frac{8}{x}+x\\ & \iff 10x^2+8+18x=80+x^2\\ & \iff 9x^2+18x-72=0\\ & \iff x^2+2x-8=0\\ & \iff \left(x+4\right)\left(x-2\right)=0\\ & \iff x=2\end{array}$$
So, ten's digit = 2 and unit's digit = 4
Hence, required number = 24