The sum of the ages of 4 children born at the intervals of 4 years is 48. Find the age of the youngest child.
A.4 years
B. 5 years.
C. 6 years
D. 7 years .

Options

A. B
B. A
C. D
D. C

Answer

To solve the problem, we need to find the age of the youngest child given that the sum of the ages of 4 children, born at intervals of 4 years, is 48.

### Step-by-Step Solution:

1. **Define the Age of the Youngest Child**:
Let the age of the youngest child be \( x \).

2. **Express the Ages of the Other Children**:
Since the children are born at intervals of 4 years, we can express their ages as follows:
- Age of the youngest child: \( x \)
- Age of the second child: \( x + 4 \)
- Age of the third child: \( x + 8 \)
- Age of the oldest child: \( x + 12 \)

3. **Set Up the Equation**:
According to the problem, the sum of their ages is 48. Therefore, we can write the equation:
\[ x + (x + 4) + (x + 8) + (x + 12) = 48 \]

4. **Simplify the Equation**:
Combine like terms:
\[ 4x + 24 = 48 \]

5. **Solve for \( x \)**:
Subtract 24 from both sides:
\[ 4x = 48 - 24 \]
\[ 4x = 24 \]
Now, divide both sides by 4:
\[ x = 6 \]

6. **Conclusion**:
The age of the youngest child is \( 6 \) years.

### Final Answer:
The age of the youngest child is **6 years** (Option C).