1. **Problem Statement:** The present age of the father is the square of the present age of his son. We need to find after how many years the son's age will be half of the present age of the father. 2. **Define variables:** Let the present age of the son be $x$ years. 3. **Express father's age:** The present age of the father is $x^2$ years. 4. **After $t$ years:** - Son's age will be $x + t$ - Father's age will be $x^2 + t$ 5. **Condition given:** After $t$ years, son's age will be half of the present age of the father. Mathematically, this is: $$x + t = \frac{1}{2} x^2$$ 6. **Solve for $t$:** $$t = \frac{1}{2} x^2 - x$$ 7. **Interpretation:** The number of years after which the son's age will be half the present age of the father is $$t = \frac{1}{2} x^2 - x$$ where $x$ is the son's current age. 8. **Note:** To find a numerical value, the son's current age $x$ must be known.