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: Let the son's present age be \( x \) years.
Then, man's present age = \( 2x \) years.
Step 2: Five years ago, son's age = \( x - 5 \), man's age = \( 2x - 5 \).
Step 3: According to the problem, five years ago:
\[ 2x - 5 = 3(x - 5) \] Step 4: Solve the equation:
\[ 2x - 5 = 3x - 15 \] \[ -5 + 15 = 3x - 2x \] \[ 10 = x \] Step 5: Son's present age \( x = 10 \) years.
Man's present age = \( 2 \times 10 = 20 \) years.
Step 6: Check options: 20 years is not listed among options. This suggests the options might be incorrect or the question may have a typo. Step 7: Among given options, none exactly fits, but algebraic solution stands.