Numbers of boys and girls are 'x' and 'y' respectively. Ages of a girl and a boy are 'a' years and 'b' years respectively. The average age (in years) of all boys and girls is:

Options

A. `(x+y)/(bx + ay)`
B. `(bx + ay)/(x+y)`
C. `(ax + by)/(x+y)`
D. `(x+y)/(ax + by)`

Answer

To find the average age of all boys and girls, we will follow these steps:

### Step 1: Understand the problem
We have:
- Number of boys = \( x \)
- Number of girls = \( y \)
- Age of a boy = \( b \) years
- Age of a girl = \( a \) years

### Step 2: Calculate the total age of boys
The total age of all boys can be calculated by multiplying the number of boys by the age of each boy:
\[ \text{Total age of boys} = x \times b \]

### Step 3: Calculate the total age of girls
Similarly, the total age of all girls can be calculated by multiplying the number of girls by the age of each girl:
\[ \text{Total age of girls} = y \times a \]

### Step 4: Calculate the total age of all boys and girls
Now, we can find the total age of all boys and girls by adding the total age of boys and girls:
\[ \text{Total age of all} = (x \times b) + (y \times a) \]

### Step 5: Calculate the total number of boys and girls
The total number of boys and girls is simply the sum of the number of boys and girls:
\[ \text{Total number of boys and girls} = x + y \]

### Step 6: Calculate the average age
Finally, we can find the average age of all boys and girls by dividing the total age by the total number of boys and girls:
\[ \text{Average age} = \frac{(x \times b) + (y \times a)}{x + y} \]

### Final Answer
Thus, the average age of all boys and girls is:
\[ \text{Average age} = \frac{(x \times b) + (y \times a)}{x + y} \]