Today Gautam, who is 36 years old, and his son who is 8 years old, celebrate their birthdays. How many years will pass before Gautama's age is thrice his son's age?

Options

A. 1. 4 years
B. 10 years
C. 6 years
D. 12 years

Answer

To solve the problem, we need to determine how many years will pass before Gautam's age is three times his son's age.

### Step-by-Step Solution:

1. **Identify Current Ages**:
- Gautam's current age = 36 years
- Son's current age = 8 years

2. **Set Up the Equation**:
- Let \( x \) be the number of years that will pass before Gautam's age is three times his son's age.
- After \( x \) years, Gautam's age will be \( 36 + x \).
- After \( x \) years, his son's age will be \( 8 + x \).

3. **Formulate the Condition**:
- We want to find \( x \) such that:
\[ 36 + x = 3(8 + x) \]

4. **Expand the Equation**:
- Expanding the right side gives:
\[ 36 + x = 24 + 3x \]

5. **Rearranging the Equation**:
- To isolate \( x \), we can rearrange the equation:
\[ 36 - 24 = 3x - x \]
- This simplifies to:
\[ 12 = 2x \]

6. **Solve for \( x \)**:
- Dividing both sides by 2 gives:
\[ x = 6 \]

### Conclusion:
After 6 years, Gautam's age will be three times his son's age.

### Final Answer:
6 years