In a class of 60 students there are 20 girls who scored an average of 40 marks in the test, what is the average marks of the boys if the class average is 60 marks?

Options

A. 60
B. 70
C. 50
D. 80

Answer

To solve the problem step by step, we will follow the information provided and perform the necessary calculations.

### Step 1: Determine the total number of students and the class average
- Total number of students in the class = 60
- Class average = 60 marks

### Step 2: Calculate the total marks of the class
To find the total marks obtained by the entire class, we can use the formula:
\[ \text{Total Marks} = \text{Number of Students} \times \text{Class Average} \]
\[ \text{Total Marks} = 60 \times 60 = 3600 \]

### Step 3: Find the number of girls and their average marks
- Number of girls = 20
- Average marks of girls = 40

### Step 4: Calculate the total marks obtained by the girls
Using the formula for total marks:
\[ \text{Total Marks of Girls} = \text{Number of Girls} \times \text{Average Marks of Girls} \]
\[ \text{Total Marks of Girls} = 20 \times 40 = 800 \]

### Step 5: Calculate the total marks obtained by the boys
To find the total marks of the boys, we subtract the total marks of the girls from the total marks of the class:
\[ \text{Total Marks of Boys} = \text{Total Marks of Class} - \text{Total Marks of Girls} \]
\[ \text{Total Marks of Boys} = 3600 - 800 = 2800 \]

### Step 6: Determine the number of boys
To find the number of boys in the class:
\[ \text{Number of Boys} = \text{Total Students} - \text{Number of Girls} \]
\[ \text{Number of Boys} = 60 - 20 = 40 \]

### Step 7: Calculate the average marks of the boys
Now, we can find the average marks of the boys using the total marks obtained by the boys and the number of boys:
\[ \text{Average Marks of Boys} = \frac{\text{Total Marks of Boys}}{\text{Number of Boys}} \]
\[ \text{Average Marks of Boys} = \frac{2800}{40} = 70 \]

Thus, the average marks of the boys is **70 marks**.