Ages Problem
- Formula / Rule
- Ages Problem
- Topic
- Algebra
- Formula
Let present age $= x$
Past/Future Age:
- n years ago: Age was $(x - n)$
- n years hence: Age will be $(x + n)$
Problem Types:
- Ratio-based: If A's age : B's age $= m : n$, represent ages as $A = mk$, $B = nk$, then form equations.
- Sum/Difference-based: Form linear equations from given sum or difference conditions and solve simultaneously.
- When to Use
- Any problem involving ages — present, past, future relationships.
- Worked Example
Q: A is 3 times as old as B. In 10 years A will be twice as old as B. Find their current ages.
Let present age of B be $B$. Then A's present age is $3B$. In 10 years: $3B+10 = 2(B+10)$ $3B+10 = 2B+20$ $B = 10$ So, $A = 3 \times 10 = 30$.
$\textbf{B=10, A=30}$