The average age of 30 students of a class is 12 yr. The average age of a group of 5 of the students is 10 yr and that of another group of 5 of them is 14 yr. what is the average age of the remaining students ?

Options

A. a) 8 yr
B. b) 10 yr
C. c) 12 yr
D. d) 14 yr

Answer

To find the average age of the remaining students, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the total age of all 30 students**:
- The average age of the 30 students is 12 years.
- Therefore, the total age of all students = Average age × Number of students = 12 years × 30 students = 360 years.

2. **Calculate the total age of the first group of 5 students**:
- The average age of the first group of 5 students is 10 years.
- Therefore, the total age of this group = Average age × Number of students = 10 years × 5 students = 50 years.

3. **Calculate the total age of the second group of 5 students**:
- The average age of the second group of 5 students is 14 years.
- Therefore, the total age of this group = Average age × Number of students = 14 years × 5 students = 70 years.

4. **Calculate the total age of the remaining students**:
- Total age of the remaining students = Total age of all students - (Total age of the first group + Total age of the second group)
- Total age of the remaining students = 360 years - (50 years + 70 years) = 360 years - 120 years = 240 years.

5. **Calculate the number of remaining students**:
- Total number of students = 30
- Number of students in the two groups = 5 + 5 = 10
- Therefore, the number of remaining students = Total number of students - Number of students in groups = 30 - 10 = 20 students.

6. **Calculate the average age of the remaining students**:
- Average age of remaining students = Total age of remaining students / Number of remaining students
- Average age = 240 years / 20 students = 12 years.

### Final Answer:
The average age of the remaining students is **12 years**.

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