The average marks obtained by the students in a class are 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?
(a)15
(b)17
(c)18
(d)20

Options

A. 15
B. 17
C. 18
D. 20

Answer

To find the number of girl students in the class, we can use the concept of averages and the relationship between the averages of boys and girls. Here’s a step-by-step solution:

### Step 1: Understand the given information
- The average marks of all students in the class = 43
- The average marks of 25 boys = 40
- The average marks of girl students = 48

### Step 2: Calculate the total marks of boys
To find the total marks obtained by the boys, we can use the formula:
\[ \text{Total Marks of Boys} = \text{Average Marks of Boys} \times \text{Number of Boys} \]
Substituting the values:
\[ \text{Total Marks of Boys} = 40 \times 25 = 1000 \]

### Step 3: Let the number of girls be \( g \)
We will denote the number of girls as \( g \).

### Step 4: Calculate the total marks of girls
Using the average marks of girls, we can find the total marks obtained by the girls:
\[ \text{Total Marks of Girls} = \text{Average Marks of Girls} \times \text{Number of Girls} \]
Substituting the values:
\[ \text{Total Marks of Girls} = 48 \times g \]

### Step 5: Calculate the total number of students
The total number of students in the class is:
\[ \text{Total Students} = \text{Number of Boys} + \text{Number of Girls} = 25 + g \]

### Step 6: Calculate the total marks of all students
The total marks of all students can also be expressed using the average marks:
\[ \text{Total Marks of All Students} = \text{Average Marks of All Students} \times \text{Total Students} \]
Substituting the values:
\[ \text{Total Marks of All Students} = 43 \times (25 + g) \]

### Step 7: Set up the equation
Now we can set up the equation based on the total marks:
\[ \text{Total Marks of Boys} + \text{Total Marks of Girls} = \text{Total Marks of All Students} \]
Substituting the values we calculated:
\[ 1000 + 48g = 43(25 + g) \]

### Step 8: Expand and simplify the equation
Expanding the right side:
\[ 1000 + 48g = 1075 + 43g \]
Now, we can simplify the equation:
\[ 1000 + 48g - 43g = 1075 \]
\[ 5g = 1075 - 1000 \]
\[ 5g = 75 \]

### Step 9: Solve for \( g \)
Now, divide both sides by 5:
\[ g = \frac{75}{5} = 15 \]

### Conclusion
The number of girl students in the class is \( \boxed{15} \).