Age Word Problem Calculator

This age word problem calculator solves a classic algebra puzzle: given two people's ages right now, in how many years will one person's age be a chosen multiple of the other's? You enter Person A's age now, Person B's age now, and the multiple k you want, so that A becomes k times B. The calculator sets up the equation A + t = k(B + t), where t is the number of years added to both ages, and solves it instantly. It returns the main result showing how far away that moment is, their two ages at that time, and whether the answer falls in the past or the future. A negative t means the relationship already happened that many years ago rather than lying ahead. There is also a check for the special case where the multiple is 1: since two people keep the same age gap forever, one age can equal the other's multiple of 1 only if they are already the same age, so the tool reports "always equal" or "never" instead of a misleading number. Try the worked example of a 40 year old and a 10 year old to see when the older is exactly twice the younger, then enter your own ages and multiple. It suits students, teachers and anyone wanting a fast, accurate answer without working through the algebra by hand.

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Person A age now

Person B age now

Multiple k (A = k x B)

Their ages then

Past or future

The formula

Let A and B be the ages now and k the multiple wanted, so that A + t = k(B + t). Solving for the time gives t = (A minus kB) / (k minus 1). A negative t means it happened that many years ago.

Worked example

If A is 40 and B is 10, when is A twice B? t = (40 minus 2 times 10) / (2 minus 1) = 20, so in 20 years A is 60 and B is 30. Enter 40, 10, 2 to confirm.

Frequently asked questions

How are age problems solved?

Add the same unknown number of years to both ages, set up the required relationship as an equation, and solve for the years.

What does a negative answer mean?

The relationship held in the past, that many years ago, rather than in the future.

Why can the multiple of 1 fail?

Two people keep the same age gap forever, so one can equal the other only if they are already the same age.

Who this calculator is for

This calculator is for students, programmers and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid input.
The standard algorithm is applied.
Results are rounded for display.

Formula and sources

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Prime Factorisation Calculator: factor a number into primes.

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