The average age of all the students of a class is 22 years. The average age of boys of the class is 24 years and that of the girls is 20 years. If the number of girls in the clss is 30, then the find the number of studnets in the class.

Answer

To solve the problem, we need to find the total number of students in the class based on the given average ages of boys and girls, along with the number of girls.

### Step-by-Step Solution:

1. **Understand the given data**:
- Average age of all students = 22 years
- Average age of boys = 24 years
- Average age of girls = 20 years
- Number of girls = 30

2. **Let the number of boys be \( b \)**.
- Therefore, the total number of students in the class = \( b + 30 \).

3. **Calculate the total age of all students**:
- Since the average age of all students is 22 years, the total age of all students can be expressed as:
\[ \text{Total age of all students} = 22 \times (b + 30) \]

4. **Calculate the total age of boys**:
- The total age of boys can be expressed as:
\[ \text{Total age of boys} = 24b \]

5. **Calculate the total age of girls**:
- The total age of girls can be expressed as:
\[ \text{Total age of girls} = 20 \times 30 = 600 \]

6. **Set up the equation**:
- The total age of all students is the sum of the total age of boys and the total age of girls:
\[ 22(b + 30) = 24b + 600 \]

7. **Expand and simplify the equation**:
- Expanding the left side:
\[ 22b + 660 = 24b + 600 \]
- Rearranging gives:
\[ 660 - 600 = 24b - 22b \]
\[ 60 = 2b \]
- Dividing both sides by 2:
\[ b = 30 \]

8. **Calculate the total number of students**:
- Now, substituting \( b \) back to find the total number of students:
\[ \text{Total students} = b + 30 = 30 + 30 = 60 \]

### Final Answer:
The total number of students in the class is **60**.

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