easymath

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?

I am 40 and my daughter is 10.

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!

Common Wrong Answers

“30 and 15”

If the father is 30, then being four times the daughter's age would make her 7.5 years old, which is not possible as ages must be whole numbers.

“50 and 10”

If the father is 50, he cannot be four times the daughter's age, as that would mean the daughter is 12.5 years old, which contradicts the father's age being 50.

“20 and 5”

If the father is 20, then he cannot be four times the daughter's age because that would make her 5 years old, and in 20 years he would be 40 and she would be 25, not twice her age.

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