The problem states that three years ago, a father was 20 years older than his son. In 10 years from now, the father will be twice as old as his son. We need to find the current age of the son and the father.

1. Problem Description

The problem states that three years ago, a father was 20 years older than his son. In 10 years from now, the father will be twice as old as his son. We need to find the current age of the son and the father.

2. Solution Steps

Let $s$ be the current age of the son and $f$ be the current age of the father.

Three years ago, the son's age was $s - 3$ and the father's age was $f - 3$. According to the problem, the father was 20 years older than the son three years ago. So,

$f - 3 = s - 3 + 20$

$f - 3 = s + 17$

$f = s + 20$ (Equation 1)

In 10 years, the son's age will be $s + 10$ and the father's age will be $f + 10$. According to the problem, the father will be twice as old as his son in 10 years. So,

$f + 10 = 2(s + 10)$

$f + 10 = 2s + 20$

$f = 2s + 10$ (Equation 2)

Now we have a system of two equations with two variables:

$f = s + 20$

$f = 2s + 10$

We can set the two expressions for $f$ equal to each other:

$s + 20 = 2s + 10$

$20 - 10 = 2s - s$

$10 = s$

So, the current age of the son is 10 years.

Now we can find the current age of the father using either Equation 1 or Equation

2. Let's use Equation 1:

$f = s + 20$

$f = 10 + 20$

$f = 30$

So, the current age of the father is 30 years.

3. Final Answer

The current age of the son is 10 years, and the current age of the father is 30 years.

The answer is A. 10 and 30 years.