Algebra Age Problems
Age problems are a classic way to test your ability to translate word problems into algebra. By following a few simple steps to define your variables, even the most complex "time-jump" questions become easy to solve.
The Rules Every Age Problem Uses
To solve any age problem, you need to turn the words into a mathematical equation. These four rules will help you structure your thinking for every question.
📝 Rule 1: Define the Unknown
Start by letting a variable (like x or P) represent the person whose age you need to find. This gives you a starting point for everything else.
Example: "How old is Peter?" → Let P = Peter's age.
👥 Rule 2: Link the Ages
Express other people's ages in terms of your first variable. If one person is "twice as old," multiply; if they are "5 years older," add.
Example: Cynthia is 4 times as old as Peter → Cynthia = 4P.
⚖️ Rule 3: Set Up the Equation
Look for a relationship like "the sum is..." or "they are equal." Use this to build your equation using the variables you defined.
Example: The sum of their ages is 65 → 4P + P = 65.
⏳ Rule 4: Handle Time Jumps
For "5 years ago" or "in 10 years," add or subtract that number from every age in the equation. Age gaps stay the same, but the values change.
Example: In 4 years, Sunil (S) will be 4 times Ravi (R) → (S + 4) = 4(R + 4).
3 Worked Examples
One straightforward, one involving the past, and one classic "simultaneous" trap.
1. Simple Age Sums
Question: Cynthia is four times as old as Peter. The sum of their ages is 65. How old is Peter?
Worked Method
Step 1: Define variables.
Let Peter's age = P
Since Cynthia is 4 times as old, her age = 4P
Step 2: Create the equation.
The sum is 65, so: 4P + P = 65
Step 3: Solve.
5P = 65
P = 65 ÷ 5 = 13
Tip: Always double check the sum. 13 + (4 × 13) = 13 + 52 = 65. It works!
2. Working with the Past
Question: Benu is currently 49 years old. 4 years ago, Benu was three times as old as Ramesh. How old is Ramesh now?
Worked Method
Step 1: Define variables.
Let Ramesh's current age = R
Step 2: Look at 4 years ago.
Benu's age then was 49 − 4 = 45.
Ramesh's age then was R − 4.
Step 3: Set up the relationship.
45 = 3(R − 4)
45 = 3R − 12
57 = 3R
Step 4: Solve for R.
R = 57 ÷ 3 = 19
Tip: Be careful with brackets! The "three times" applies to Ramesh's entire age 4 years ago, not just the current age.
3. The Double Time-Jump
Question: Sunil is 45 years older than Ravi. In 4 years' time, Sunil will be four times as old as Ravi. How old is Ravi now?
Worked Method
Step 1: Define current ages.
Let Ravi = R
Sunil = R + 45
Step 2: Add 4 years to BOTH.
In 4 years, Ravi = R + 4
In 4 years, Sunil = (R + 45) + 4 = R + 49
Step 3: Set up the new relationship.
R + 49 = 4(R + 4)
R + 49 = 4R + 16
33 = 3R
Step 4: Solve.
R = 11
The Trap: Many students forget to add 4 years to both people. Sunil gets older, but so does Ravi!
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
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The full pack has 90 algebra age problems across 3 test sets, covering everything from basic sums to complex time-based riddles. Step-by-step solutions included for every question.
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