13. (15 points) If number $A$ is increased by 2, then its product with number $B$ is 60 more than the product of $A$ and $B$; if number $A$ remains unchanged and number $B$ is decreased by 3, then their product is 24 less than the product of $A$ and $B$. Therefore, if number $A$ is increased by 2 and number $B$ is decreased by 3, how much more is their product compared to the product of $A$ and $B$?
【Analysis】These two numbers are $A$ and $B$. From "If number $A$ is increased by 2, then its product with number $B$ is 60 more than the product of $A$ and $B$", we can set up an equation to solve for $A$ and $B$. Then, based on "If number $A$ is increased by 2 and number $B$ is decreased by 3", we substitute $A$ and $B$ to find out how much greater their product is compared to the product of $A$ and $B$.
【Solution】Solution: These two numbers are $A$ and $B$, we can get:
$$
A B+60=(A+2) \times B, A B-24=A(B-3) ;
$$

Since $A B+60=(A+2) \times B$
Then $A B+60=A B+2 B$

Then $B=30$
Substituting $B=30$ into $A B-24=A(B-3)$, we get:
$$
\begin{array}{c}
30 A-24=A(30-3) \\
30 A-24=27 A \\
A=8
\end{array}
$$
$$
\begin{aligned}
& (8+2) \times(30-3)-30 \times 8 \\
= & 10 \times 27-240 \\
= & 30
\end{aligned}
$$

Answer: Their product is 30 more than the product of $A$ and $B$.