There were 24 students in a class. One of them, who was 18 years old, left the class and his place was filled up by a newcomer. If the average of the class thereby, was lowered by one month, the age of the newcomer is:

Options

A. 14 years
B. 15 years
C. 16 years
D. 17 years

Answer

To solve the problem step by step, we will analyze the situation involving the class of students and the changes in their average age.

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- There are 24 students in the class.
- One student, who is 18 years old, leaves the class.

2. **Understanding the Change in Average:**
- The average age of the class decreases by one month when the newcomer replaces the 18-year-old student.
- Since the average is given in years, we convert one month into years: 1 month = 1/12 years.

3. **Calculate the Total Age Reduction:**
- Since the average age decreases by 1 month for 24 students, the total reduction in age can be calculated as:
\[ \text{Total reduction} = \text{Number of students} \times \text{Reduction in average age} = 24 \times \frac{1}{12} = 2 \text{ years} \]

4. **Determine the Newcomer's Age:**
- The total age of the class decreases by 2 years because one student aged 18 leaves and is replaced by the newcomer.
- Let the age of the newcomer be \( x \).
- The new total age of the class can be expressed as:
\[ \text{New total age} = \text{Old total age} - 18 + x \]
- Since the total age decreases by 2 years, we can set up the equation:
\[ -18 + x = -2 \]
- Rearranging gives:
\[ x = 18 - 2 = 16 \]

5. **Conclusion:**
- The age of the newcomer is 16 years.

### Final Answer:
The age of the newcomer is **16 years**.

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