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?

Options

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

Explanation

To solve the problem, we need to find the number of girl students in the class based on the given average marks. Let's break it down step by step.

### Step 1: Understand the given information
- Average marks of the entire class = 43
- Average marks of 25 boys = 40
- Average marks of girl students = 48
- Let the number of girl students be \( x \).

### Step 2: Calculate the total marks obtained by boys
The total marks obtained by the boys can be calculated using the formula:
\[ \text{Total marks by boys} = \text{Number of boys} \times \text{Average marks of boys} \]
Substituting the values:
\[ \text{Total marks by boys} = 25 \times 40 = 1000 \]

### Step 3: Calculate the total marks obtained by girls
The total marks obtained by the girls can be calculated using the formula:
\[ \text{Total marks by girls} = \text{Number of girls} \times \text{Average marks of girls} \]
Substituting the values:
\[ \text{Total marks by girls} = x \times 48 \]

### Step 4: Set up the equation for the average marks of the entire class
The average marks of the entire class can be expressed as:
\[ \text{Average} = \frac{\text{Total marks by boys} + \text{Total marks by girls}}{\text{Total number of students}} \]
Substituting the known values:
\[ 43 = \frac{1000 + 48x}{25 + x} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 43(25 + x) = 1000 + 48x \]

### Step 6: Expand and simplify the equation
Expanding the left side:
\[ 1075 + 43x = 1000 + 48x \]

### Step 7: Rearrange the equation to isolate \( x \)
Rearranging gives:
\[ 1075 - 1000 = 48x - 43x \]
\[ 75 = 5x \]

### Step 8: Solve for \( x \)
Dividing both sides by 5:
\[ x = \frac{75}{5} = 15 \]

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

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