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 :

Solution(By Examveda Team)

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