There are 30 students in a class .The average age of the first 10 students is 12.5 years .The average age of the remaining 20 students is 13.1 years .What is the average age (in years ) of the students of the whole class ?

Answer

To find the average age of all the students in the class, we can follow these steps:

### Step 1: Calculate the total age of the first 10 students.
Given:
- Average age of the first 10 students = 12.5 years
- Number of students = 10

Using the formula for average:
\[ \text{Average} = \frac{\text{Total Sum of Ages}}{\text{Number of Students}} \]
We can rearrange this to find the total sum of ages:
\[ \text{Total Sum of Ages} = \text{Average} \times \text{Number of Students} \]
So for the first 10 students:
\[ \text{Total Sum of Ages} = 12.5 \times 10 = 125 \text{ years} \]

### Step 2: Calculate the total age of the remaining 20 students.
Given:
- Average age of the remaining 20 students = 13.1 years
- Number of students = 20

Using the same formula:
\[ \text{Total Sum of Ages} = 13.1 \times 20 = 262 \text{ years} \]

### Step 3: Calculate the total age of all students in the class.
Now, we need to find the total age of all 30 students:
\[ \text{Total Age of All Students} = \text{Total Age of First 10 Students} + \text{Total Age of Remaining 20 Students} \]
\[ \text{Total Age of All Students} = 125 + 262 = 387 \text{ years} \]

### Step 4: Calculate the average age of the whole class.
Now, we can find the average age of all 30 students:
\[ \text{Average Age} = \frac{\text{Total Age of All Students}}{\text{Total Number of Students}} = \frac{387}{30} \]
Calculating this gives:
\[ \text{Average Age} = 12.9 \text{ years} \]

### Final Answer:
The average age of the students in the whole class is **12.9 years**.

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