Who talks like that?

We can call the current age of the older man X, the age of the younger Y. Then we can solve this system

X-10=3(Y-10)

X+10=2(Y+10)

Solving this system we find that X=70, Y=30. So the answer is 30

Let's assume that $x$ and $y$ are the current ages of the older man and the younger man, now we can write:

$\large \begin{cases} x -10 & = 3(y-10) ~~~~ .....(1) \\ x +10 & = 2(y+10) ~~~~ .....(2) \\ \end{cases}$

Now, from $(1):$

$\begin{aligned} x-10 & = 3(y - 10) \\ x & = 3y - 30 +10 \\ x & = 3y - 20 ~~~~ .....(3).\\ \end{aligned}$

Substituting $x = 3y - 20$ in $(2):$

$\begin{aligned} 3y - 20 +10 &= 2y + 20 \\ 3y - 10 & = 2y + 20 \\ 3y - 2y & = 20 + 10 \\ \implies y & = \boxed{30}.\\ \end{aligned}$

Hence the current age of the younger man is 30 years. We don't have to solve for $x$ now.