In a class there were 9 boys and some girls. In a test the mean score obtained by the boys was 13 while that obtaind by the girls was 15. If the overall average was 14.28 what was the total number of students in the class?

Options

A. 24
B. 26
C. 27
D. 25

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Define Variables
Let the number of girls in the class be represented by \( X \). We know there are 9 boys.

### Step 2: Calculate the Total Marks for Boys
The mean score of the boys is 13. Therefore, the total marks obtained by the boys can be calculated as:
\[ \text{Total Marks of Boys} = \text{Mean} \times \text{Number of Boys} = 13 \times 9 = 117 \]

### Step 3: Calculate the Total Marks for Girls
The mean score of the girls is 15. Therefore, the total marks obtained by the girls can be calculated as:
\[ \text{Total Marks of Girls} = \text{Mean} \times \text{Number of Girls} = 15 \times X \]

### Step 4: Calculate the Overall Average
The overall average score of the class is given as 14.28. The total number of students in the class is \( 9 + X \) (boys + girls). The formula for the overall average is:
\[ \text{Overall Average} = \frac{\text{Total Marks of Boys} + \text{Total Marks of Girls}}{\text{Total Number of Students}} \]
Substituting the known values:
\[ 14.28 = \frac{117 + 15X}{9 + X} \]

### Step 5: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 14.28(9 + X) = 117 + 15X \]

### Step 6: Distribute and Rearrange the Equation
Distributing \( 14.28 \):
\[ 128.52 + 14.28X = 117 + 15X \]
Now, rearranging the equation:
\[ 128.52 - 117 = 15X - 14.28X \]
\[ 11.52 = 0.72X \]

### Step 7: Solve for \( X \)
Now, divide both sides by 0.72:
\[ X = \frac{11.52}{0.72} = 16 \]

### Step 8: Calculate Total Number of Students
Now that we have \( X \), which is the number of girls, we can find the total number of students:
\[ \text{Total Students} = \text{Number of Boys} + \text{Number of Girls} = 9 + 16 = 25 \]

### Final Answer
The total number of students in the class is **25**.

---