Algebra Age Problems Practice Test Worksheets
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.
For students who can solve simple equations, but get stuck turning age word problems into the right algebra.
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What Do Age Problems Questions Look Like?
Algebra age problems ask you to determine the unknown age of one or more people using a set of comparative clues and time shifts. The challenge lies in translating the wording into clear linear equations before solving. Here is a worked example.
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 current 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!
Rules to Help You Solve Age Problems Questions
To solve age problems like the example above, you need to turn the words into structured equations. Follow these four rules to organise your steps:
📝 Rule 1: Define the Unknown
Start by letting a variable (like x or P) represent a person's current age in years. Use this as your starting point for expressing ages at other times.
Example: "How old is Peter now?" → Let P = Peter's current age in years.
👥 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's current age = 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 each person, subtract years from their current age to describe the past, or add years to describe the future. Check which time each age refers to. When comparing both people at the same future or past time, shift both ages by the same number of years. Their age gap stays the same.
Example: Let S and R be Sunil's and Ravi's current ages. In 4 years, Sunil will be 4 times as old as Ravi → S + 4 = 4(R + 4).
Two More Worked Examples
Here are two more examples demonstrating how to navigate past time jumps and compare future ages without getting tripped up.
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.
Comparing Future Ages
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's current age = R
Sunil's current age = 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!
