I am four times as old as my daughter. In 20 years time I shall be twice as old as her. How old are we now?

Why this works

This riddle is a classic age problem that can be solved using algebra. Let's break it down: if we let the father's current age be \( F \) and the daughter's age be \( D \), the first part tells us that \( F = 4D \). The second part states that in 20 years, the father's age will be \( F + 20 \) and the daughter's age will be \( D + 20 \). According to the riddle, at that time, the father will be twice the daughter's age: \( F + 20 = 2(D + 20) \). By substituting \( F = 4D \) into the second equation, we can solve for \( D \) and find that \( D = 10 \), leading us to \( F = 40 \). Thus, the father is 40 years old and the daughter is 10, illustrating how cleverly age relationships can be expressed through simple equations!