Certainly! Let’s solve this step-by-step:
1. Identify the given information:
- Total number of students in the class: 24
- Number of boys: 10
- Mean mark of the boys: 57%
- Mean mark of the entire class: 62%
2. Calculate the total marks obtained by the boys:
- The mean mark of the boys is 57%.
- Therefore, the total marks obtained by all the boys combined is:
[tex]\( \text{Total marks of boys} = \text{Number of boys} \times \text{Mean mark of boys} \)[/tex]
[tex]\[
\text{Total marks of boys} = 10 \times 57 = 570
\][/tex]
3. Calculate the total marks obtained by the entire class:
- The mean mark of the entire class is 62%.
- Therefore, the total marks obtained by the entire class combined is:
[tex]\( \text{Total marks of class} = \text{Total number of students} \times \text{Mean mark of class} \)[/tex]
[tex]\[
\text{Total marks of class} = 24 \times 62 = 1488
\][/tex]
4. Calculate the total marks obtained by the girls:
- We know the total marks for the entire class and the total marks obtained by the boys.
- Therefore, the total marks obtained by the girls is:
[tex]\[
\text{Total marks of girls} = \text{Total marks of class} - \text{Total marks of boys}
\][/tex]
[tex]\[
\text{Total marks of girls} = 1488 - 570 = 918
\][/tex]
5. Calculate the number of girls in the class:
- The total number of students is 24 and the number of boys is 10.
- Therefore, the number of girls is:
[tex]\[
\text{Number of girls} = \text{Total number of students} - \text{Number of boys}
\][/tex]
[tex]\[
\text{Number of girls} = 24 - 10 = 14
\][/tex]
6. Calculate the mean mark obtained by the girls:
- The mean mark is calculated by dividing the total marks by the number of students.
- Therefore, the mean mark obtained by the girls is:
[tex]\[
\text{Mean mark of girls} = \frac{\text{Total marks of girls}}{\text{Number of girls}}
\][/tex]
[tex]\[
\text{Mean mark of girls} = \frac{918}{14} \approx 65.57
\][/tex]
So, the mean mark achieved by the girls for this test is approximately 65.57%.
