Define variables for the current ages.

Let the current age of the father be $F$ years.
Let the current age of the son be $S$ years.

According to the first condition, 10 years ago, the father's age was three times the son's age.
Father's age 10 years ago: $F - 10$
Son's age 10 years ago: $S - 10$
So, we have the equation:

According to the second condition, 10 years from now, the father's age will be twice the son's age.
Father's age 10 years from now: $F + 10$
Son's age 10 years from now: $S + 10$
So, we have the equation:

We have two expressions for $F$. Equate them:

Subtract $2S$ from both sides:

Add 20 to both sides:

The current age of the son is 30 years.

Now substitute $S = 30$ into equation $(**)$ to find $F$:

The current age of the father is 70 years.

The ratio of the father's current age to the son's current age is $\frac{F}{S}$.

The ratio of their current ages is $7:3$.