The ratio of the ages of $A$ and $B$ is $3:2$. Ten years hence, the sum of their ages will be $80$. What are their respective present ages (in years)?

Let the present ages of $A$ and $B$ be $3x$ and $2x$ years respectively, based on the given ratio $3:2$.
Ten years hence:
Age of $A=3x+10$
Age of $B=2x+10$

According to the question, the sum of their ages ten years hence will be $80$:

$$(3x+10)+(2x+10)=80$$

$$5x+20=80$$

$$5x=60$$

$$x=\frac{60}{5}=12$$

Now, calculate their present ages:
Present age of $A=3x=3\times 12=36\text{years}$
Present age of $B=2x=2\times 12=24\text{years}$