Question

Five years ago, A was three times as old as B. Now, A is twice as old as B. What is A's current age?

• A. 20
• B. 15
• C. 25
• D. 30

Hint:

Set variables for "Current Age" to avoid confusion with "X years ago".

Answer 1

The Correct Option is A

Step 1: Choose variables for present ages.
Let B's current age be $b$. Since A is now twice as old as B, A's current age is $2b$.
Step 2: Shift back five years.
Five years ago A was $2b - 5$ and B was $b - 5$.
Step 3: Use the past relation.
Five years ago A was three times B, so $2b - 5 = 3(b - 5)$.
Step 4: Expand and simplify.
$2b - 5 = 3b - 15$. Bringing terms together gives $15 - 5 = 3b - 2b$, so $10 = b$.
Step 5: Find A's age.
A is $2b = 2 \times 10 = 20$ years old now.
Step 6: Verify both conditions.
Now A is 20 and B is 10, so A is twice B, correct. Five years ago A was 15 and B was 5, and $15 = 3 \times 5$, correct. So A's current age is 20, matching option 1.
\[ \boxed{20} \]