The average age of the boys in a class is 18 years. The average age of the girls in that class is 12 years. If the ratio of the number of boys and girls in that class Is 3 : 2, then the average age of the class is :

Options

A. 15. 6 years
B. 16. 5 years
C. 15 years
D. 16 years

Answer

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

### Step 1: Understand the given information
- Average age of boys = 18 years
- Average age of girls = 12 years
- Ratio of boys to girls = 3:2

### Step 2: Assign variables based on the ratio
Let the number of boys be \(3x\) and the number of girls be \(2x\), where \(x\) is a common multiplier.

### Step 3: Calculate the total age of boys
The total age of boys can be calculated as:
\[ \text{Total age of boys} = \text{Average age of boys} \times \text{Number of boys} \]
\[ = 18 \times 3x = 54x \]

### Step 4: Calculate the total age of girls
The total age of girls can be calculated as:
\[ \text{Total age of girls} = \text{Average age of girls} \times \text{Number of girls} \]
\[ = 12 \times 2x = 24x \]

### Step 5: Calculate the total age of the class
Now, we can find the total age of the entire class by adding the total ages of boys and girls:
\[ \text{Total age of class} = \text{Total age of boys} + \text{Total age of girls} \]
\[ = 54x + 24x = 78x \]

### Step 6: Calculate the total number of students in the class
The total number of students in the class is:
\[ \text{Total number of students} = \text{Number of boys} + \text{Number of girls} \]
\[ = 3x + 2x = 5x \]

### Step 7: Calculate the average age of the class
Finally, the average age of the class can be calculated as:
\[ \text{Average age of class} = \frac{\text{Total age of class}}{\text{Total number of students}} \]
\[ = \frac{78x}{5x} = \frac{78}{5} = 15.6 \text{ years} \]

### Final Answer
The average age of the class is **15.6 years**.

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