Age Problem Calculator (In How Many Years)

A parent is now a certain age and their child another. Find in how many years the parent will be exactly a chosen multiple of the child age. This classic word problem uses the constant age difference and shows the solving steps.

Input

Enter the current parent and child ages and a multiple to find in how many years the parent age becomes exactly that many times the child age.

Parent age now

Child age now

Multiple

How many times older the parent should be (greater than 1).

Result

That multiple happens in

20 years

Parent age then

60 yr

Child age then

30 yr

Age difference

30 yr

How to solve it

First find the age difference. It is 30 years and never changes over time.

When the parent is 2 times the child, treat the child age as 1 part and the parent as 2 parts, so the difference equals the age difference.

Splitting the age difference this way gives the child as 30 yr and the parent as 60 yr at that time.

Compared with the current ages, this happens 20 years from now.

The child age at that time equals the age difference divided by the multiple minus one, and its gap from the current child age gives the number of years.

How it works

In age problems the difference between the parent and child age never changes. Because that difference is constant, you can find the target year from the multiple condition.
When the parent age is exactly the chosen multiple of the child age, the child age at that time equals the age difference divided by the multiple minus one.
A positive result means years in the future and a negative result means years in the past. If the answer is not a whole number, the tool notes that no whole year satisfies the condition.

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