CE Board Exam Randomizer

Age Problems

Age problems involve translating relationships about people’s ages — either in the present, past, or future — into algebraic expressions or equations.

Common Phrases in Age Problems:

• "x years ago" → Subtract: $x - \text{years}$
• "in x years" → Add: $x + \text{years}$
• "Twice as old" → Multiply: $2x$
• "Half as old" → Divide: $\frac{x}{2}$
• "The difference in age" → Subtract one from the other

Typical Structure:

Let one person’s age be a variable (e.g., $x$), and express the others in terms of $x$.

Problem 1:

Itadori is 4 years younger than Megumi. Twenty years ago, Megumi’s age was 13 years more than half the age of Itadori. How old are they now?

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Problem 2:

When I am as old as my father is now, I shall be five times as old as my son is now. By then, my son will be eight years older than I am now. The combined ages of my father and me is 100 years. How old is my son?

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Problem 3:

Six years ago, Tom was five times as old as Ana. In five years, Tom will be three times as old as Ana. What is the present age of Ana?

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Problem 4:

If Luna was four times as old as Lina eight years ago, and if Luna will be twice as old as Lina eight years hence, how old is Lina now?

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Problem 5:

Rumi is three times as old as Zoey. Three years ago, she is four times as old as Zoey. Find the sum of their ages. Ans. 36

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