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 $2x$ respectively.
Ten years hence:
Age of A = $3x+10$
Age of B = $2x+10$

According to the question, the sum of their ages after 10 years will be $80$:

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

$$5x+20=80$$

$$5x=60$$

$$x=12$$

Therefore, their present ages are:
Present age of A = $3\times 12=36$ years
Present age of B = $2\times 12=24$ years