Question

If a father age is three times to his son's age. After 20 years it became two times of his son age. What is the age of son now?

Answer 1

Let the current age of the son be \( x \). Then the current age of the father is \( 3x \) (since the father is three times the son's age).

In 20 years, the son's age will be \( x + 20 \) and the father's age will be \( 3x + 20 \).

According to the problem, after 20 years, the father's age will be twice the son's age. This gives us the equation:

\[
3x + 20 = 2(x + 20)
\]

Now, let's expand and solve this equation:

\[
3x + 20 = 2x + 40
\]

Subtract \( 2x \) from both sides:

\[
3x - 2x + 20 = 40
\]

This simplifies to:

\[
x + 20 = 40
\]

Now, subtract 20 from both sides:

\[
x = 20
\]

So, the current age of the son is \( 20 \) years.

To confirm:
- Current age of the son: \( 20 \)
- Current age of the father: \( 3 \times 20 = 60 \)

In 20 years:
- Son's age: \( 20 + 20 = 40 \)
- Father's age: \( 60 + 20 = 80 \)

Indeed, \( 80 \) is twice \( 40 \).

Thus, the son's current age is \( \boxed{20} \) years.