In an examination average marks obtained by the girls of a class is 85 and the average marks obtained by the boys of the same class is 87. If the girls and boys are in the ratio 4:5, average marks of the whole class (approximately) is closest to

Options

A. 85.9
B. 86.1
C. 86.4
D. 86.5

Answer

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

### Step 1: Define the Variables
Let the number of girls be \(4x\) and the number of boys be \(5x\) based on the given ratio of girls to boys (4:5).

### Step 2: Calculate Total Marks for Girls
The average marks obtained by the girls is 85. Therefore, the total marks obtained by the girls can be calculated as:
\[ \text{Total Marks of Girls} = \text{Average Marks of Girls} \times \text{Number of Girls} = 85 \times 4x = 340x \]

### Step 3: Calculate Total Marks for Boys
The average marks obtained by the boys is 87. Therefore, the total marks obtained by the boys can be calculated as:
\[ \text{Total Marks of Boys} = \text{Average Marks of Boys} \times \text{Number of Boys} = 87 \times 5x = 435x \]

### Step 4: Calculate Total Marks of the Class
Now, we can find the total marks of the whole class by adding the total marks of girls and boys:
\[ \text{Total Marks of Class} = \text{Total Marks of Girls} + \text{Total Marks of Boys} = 340x + 435x = 775x \]

### Step 5: Calculate Total Number of Students
The total number of students in the class is:
\[ \text{Total Students} = \text{Number of Girls} + \text{Number of Boys} = 4x + 5x = 9x \]

### Step 6: Calculate Average Marks of the Whole Class
Finally, we can calculate the average marks of the whole class by dividing the total marks by the total number of students:
\[ \text{Average Marks of Class} = \frac{\text{Total Marks of Class}}{\text{Total Students}} = \frac{775x}{9x} = \frac{775}{9} \approx 86.11 \]

Thus, the average marks of the whole class (approximately) is closest to **86**.

---