In a class of 45 students boys and girls are in the ratio of 5: 4 respectively. Average marks obtained by boys in Mathematics out of 100 were 76 and that of girls were 78. What are average marks of boys and girls together in Mathematics (round of to two decimal points)?

Options

A. `76 cdot 89`
B. 77
C. `77 cdot 29`
D. `76 cdot 98`

Answer

To find the average marks of boys and girls together in Mathematics, we will follow these steps:

### Step 1: Determine the number of boys and girls in the class
Given the ratio of boys to girls is 5:4, we can let the number of boys be 5x and the number of girls be 4x. The total number of students is 45.

\[ 5x + 4x = 45 \]

### Step 2: Solve for x
Combine the terms:

\[ 9x = 45 \]

Now, divide both sides by 9:

\[ x = 5 \]

### Step 3: Calculate the number of boys and girls
Now substitute x back to find the number of boys and girls:

- Number of boys = \(5x = 5 \times 5 = 25\)
- Number of girls = \(4x = 4 \times 5 = 20\)

### Step 4: Calculate the total marks obtained by boys and girls
The average marks obtained by boys is 76, and the average marks obtained by girls is 78.

- Total marks obtained by boys = Number of boys × Average marks of boys
\[ = 25 \times 76 = 1900 \]

- Total marks obtained by girls = Number of girls × Average marks of girls
\[ = 20 \times 78 = 1560 \]

### Step 5: Calculate the total marks obtained by all students
Now, add the total marks of boys and girls:

\[ \text{Total marks} = 1900 + 1560 = 3460 \]

### Step 6: Calculate the average marks of boys and girls together
Now, to find the average marks of all students together, divide the total marks by the total number of students:

\[ \text{Average marks} = \frac{\text{Total marks}}{\text{Total number of students}} = \frac{3460}{45} \approx 76.78 \]

### Step 7: Round off to two decimal points
The average marks of boys and girls together in Mathematics, rounded to two decimal points, is:

\[ \text{Average marks} \approx 76.78 \]

### Final Answer
The average marks of boys and girls together in Mathematics is **76.78**.

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