1. **State the problem:** A father is 4 times as old as his son. In 20 years, the father will be twice as old as his son. We need to find their present ages. 2. **Define variables:** Let the son's present age be $x$ years. 3. **Express the father's age:** Since the father is 4 times as old as his son, the father's present age is $4x$ years. 4. **Set up the equation for ages in 20 years:** In 20 years, the son's age will be $x + 20$ and the father's age will be $4x + 20$. 5. **Use the condition given:** The father will be twice as old as the son in 20 years, so: $$4x + 20 = 2(x + 20)$$ 6. **Solve the equation:** $$4x + 20 = 2x + 40$$ 7. **Bring all terms to one side:** $$4x + 20 - 2x - 40 = 0$$ $$2x - 20 = 0$$ 8. **Simplify:** $$2x = 20$$ 9. **Divide both sides by 2:** $$\cancel{2}x = \cancel{2}10$$ $$x = 10$$ 10. **Find the father's age:** $$4x = 4 \times 10 = 40$$ **Final answer:** The son is 10 years old and the father is 40 years old.