Age Word Problem Calculator
In how many years will one person be a given multiple of another’s age? Solve the classic "times as old" age puzzle with the algebra shown.
How it works
A + n = k · (B + n) → n = (A − k·B) ÷ (k − 1)
Both people age at the same rate, so add the same unknown n to each current age and set A’s future age equal to k times B’s. Solving that single equation gives n directly. A negative n is a real answer — it means the ratio held that many years in the past rather than the future, because age ratios drift toward 1 as everyone gets older.
Worked example
A parent is 40 and a child is 10; when will the parent be twice the child’s age? Solve 40 + n = 2(10 + n): 40 + n = 20 + 2n, so n = 20. In 20 years the parent is 60 and the child 30 — exactly double.
Frequently asked questions
Why is the multiple of 1 not allowed?
Being “1 times as old” means the ages are equal. Two people with different ages never have equal ages, and two with equal ages always do, so there is no single year that answers it — the formula divides by zero.
What does a negative answer mean?
It means the condition was true in the past, not the future. For example, an older sibling was twice the younger one’s age some years ago; going forward the ratio only shrinks toward 1.
Can the multiple be a decimal like 1.5?
Yes. Any positive multiple other than 1 works — 1.5×, 3×, or a fraction below 1 if you swap who is older. The algebra is identical.
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