A class has 20 boys and 30 girls. The average age of boys is 11 years and that of girls is 12 years. What is the average age of the whole class

Options

A. 11.6 years
B. 12 years
C. 10 years
D. 11.2 years

Answer

To find the average age of the whole class, we can follow these steps:

### Step 1: Calculate the total age of boys
The average age of boys is given as 11 years, and there are 20 boys in the class.
To find the total age of the boys, we multiply the average age by the number of boys.

\[ \text{Total age of boys} = \text{Average age of boys} \times \text{Number of boys} = 11 \times 20 = 220 \text{ years} \]

### Step 2: Calculate the total age of girls
The average age of girls is given as 12 years, and there are 30 girls in the class.
To find the total age of the girls, we multiply the average age by the number of girls.

\[ \text{Total age of girls} = \text{Average age of girls} \times \text{Number of girls} = 12 \times 30 = 360 \text{ years} \]

### Step 3: Calculate the total age of the whole class
Now, we can find the total age of the whole class by adding the total age of boys and the total age of girls.

\[ \text{Total age of class} = \text{Total age of boys} + \text{Total age of girls} = 220 + 360 = 580 \text{ years} \]

### Step 4: Calculate the total number of students
Next, we find the total number of students in the class by adding the number of boys and girls.

\[ \text{Total number of students} = \text{Number of boys} + \text{Number of girls} = 20 + 30 = 50 \]

### Step 5: Calculate the average age of the whole class
Finally, we can find the average age of the whole class by dividing the total age of the class by the total number of students.

\[ \text{Average age of class} = \frac{\text{Total age of class}}{\text{Total number of students}} = \frac{580}{50} = 11.6 \text{ years} \]

### Conclusion
The average age of the whole class is **11.6 years**.

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