Smaller number

If the two numbers are $x+9, y+9$ , then

$\dfrac{x+9}{3}=\dfrac{y+9}{5}$ $\Rightarrow 5x+45=3y+27$

$\dfrac{y}{23}=\dfrac{x}{12}$ $\Rightarrow 12y=23x$

Adding the left sides and the right sides together of the equations above, we get:

$(5x+45)+(12y)=(3y+27)+(23x)$

If we subtract $5x+3y+27$ from both sides, we get:

$9y+18=18x$ $\Rightarrow y+2=2x$ $\Rightarrow x=\dfrac{y+2}{2}$

So substituting it to the $12y=23x$ , we get:

$12y=23\dfrac{y+2}{2}$ $\Rightarrow 24y=23y+46$ $\Rightarrow y=46$ $\Rightarrow x=\dfrac{y+2}{2}=48/2=24$

Since $24<46$ ,

$\text{answer}=24+9=\boxed{33}$