Age Problem Calculator (Find Current Ages)
Solve the classic age word problem: from the age difference, a number of years later, and a multiple, find the current ages of parent and child.
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Input
Enter the age difference, how many years later, and how many times the parent is the child to find their current ages.
Enter the difference as a positive whole number, the years as 0 or more, and the multiple as 2 or more.
Result
Current ages
Child now
10 years
Parent now
38 years
How to solve
The difference never changes. If the child age is x, the parent is x + 28.
Write the condition that the parent is 3 times the child 4 years later.
Solving gives the child current age ( 28 minus 4 times ( 3 minus 1 ) ) / ( 3 minus 1 ) = 10 years.
The parent adds the difference back: 10 + 28 = 38 years.
Check
Child in 4 years
14 years
Parent in 4 years
42 years
42 divided by 14 = 3, so the condition holds.
How it works
- The age difference stays the same as time passes. If the child current age is x and the difference is D, the parent current age is x + D.
- After n years the child is x + n and the parent is x + D + n. The parent being m times the child gives ( x + D ) + n = m times ( x + n ).
- Rearranging gives x = ( D minus n times ( m minus 1 ) ) / ( m minus 1 ), which is the child current age. The parent age adds the difference back.
- If the child age is not a whole number that is 0 or more, the puzzle has no valid answer and the tool explains this.
- Enter the multiple m as a whole number of 2 or more, the difference as a positive whole number, and the years as a whole number of 0 or more.
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