Question

A father is 10 years older than his son. In 10 years, his age will be 1.5 times his son’s age. What is the present age of the father?

• A. 20 years
• B. 35 years
• C. 25 years
• D. 30 years

Hint:

In age-related problems, always express future ages clearly and convert verbal statements like “times” into mathematical equations carefully.

Answer 1

The Correct Option is A

Step 1: Assume the present age of the son.
Let the present age of the son be \( x \) years.
Then, the present age of the father will be \( x + 10 \) years.
Step 2: Write the ages after 10 years.
After 10 years, the son’s age will be \( x + 10 \) years.
After 10 years, the father’s age will be \( x + 20 \) years.
Step 3: Form the equation using the given condition.
According to the question, after 10 years, the father’s age will be 1.5 times the son’s age.
\[ x + 20 = 1.5(x + 10) \]
Step 4: Solve the equation.
\[ x + 20 = 1.5x + 15 \]
\[ 20 - 15 = 1.5x - x \]
\[ 5 = 0.5x \]
\[ x = 10 \]
Step 5: Find the present age of the father.
Present age of the father = \( x + 10 = 10 + 10 = 20 \) years.
Step 6: Conclusion.
The present age of the father is 20 years.