Question

A man’s present age is twice his son's age. Five years ago, the man's age was three times his son's age. What is the man's present age?

• A. 30 years
• B. 40 years
• C. 45 years
• D. 50 years

Hint:

Use algebraic variables for ages and form equations based on given relationships to find unknown ages.

Answer 1

The Correct Option is C

Step 1: Define variables: Let the son's current age be \( x \) years. Consequently, the man's current age is \( 2x \) years.
Step 2: Determine ages five years prior: The son's age was \( x - 5 \) years, and the man's age was \( 2x - 5 \) years.
Step 3: Formulate the equation based on the problem statement: Five years ago, the man's age was three times the son's age. This yields the equation:
\[2x - 5 = 3(x - 5)\]Step 4: Solve the algebraic equation:
\[2x - 5 = 3x - 15\]Rearranging terms:
\[-5 + 15 = 3x - 2x\]Simplifying:
\[10 = x\]Step 5: Calculate current ages: The son's current age is \( x = 10 \) years. The man's current age is \( 2 \times 10 = 20 \) years.
Step 6: Evaluate against provided options: The calculated man's age of 20 years is not present in the given options, indicating a potential issue with the options or the question's phrasing.
Step 7: Conclusion on options: While no provided option matches the derived answer, the algebraic solution remains valid.