A father is 40years older than his son a son is 12years in how many years will be twice son's age and prove the answer

Let the son's current age be $S$ and the father's current age be $F$.
Given that the son is 12 years old:

$$S = 12 \text{ years}$$

Given that the father is 40 years older than his son:

$$F = S + 40$$ $$F = 12 + 40 = 52 \text{ years}$$

So, currently, the son is 12 years old and the father is 52 years old.

Let $x$ be the number of years from now when the father will be twice the son's age.
In $x$ years, the son's age will be $S + x = 12 + x$.
In $x$ years, the father's age will be $F + x = 52 + x$.
According to the problem, in $x$ years, the father's age will be twice the son's age:

$$52 + x = 2(12 + x)$$

$$52 + x = 24 + 2x$$

Subtract $x$ from both sides:

$$52 = 24 + 2x - x$$ $$52 = 24 + x$$

Subtract 24 from both sides:

$$x = 52 - 24$$ $$x = 28$$

The father will be twice the son's age in $\boxed{28 \text{ years}}$.

In 28 years:
Son's age will be $12 + 28 = 40$ years.
Father's age will be $52 + 28 = 80$ years.
Check if the father's age is twice the son's age:

$$80 = 2 \times 40$$ $$80 = 80$$

The condition is satisfied, proving the answer is correct.

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