Class 10 R sat a test. The mean mark for the class was \( 70 \% \). There are 30 students in class \( 10 \mathrm{R}, 20 \) of whom are boys. The mean mark for the boys in the test was \( 62 \% \). Work out the mean mark for the girls.

To find the mean mark for the girls in Class 10 R, we can use the information provided about the overall mean and the mean for the boys. 1. **Calculate the total marks for the class**: The mean mark for the class is \( 70\% \) with 30 students. \[ \text{Total marks for the class} = \text{Mean} \times \text{Number of students} = 70 \times 30 = 2100. \] 2. **Calculate the total marks for the boys**: The mean mark for the boys is \( 62\% \) with 20 boys. \[ \text{Total marks for the boys} = \text{Mean} \times \text{Number of boys} = 62 \times 20 = 1240. \] 3. **Calculate the total marks for the girls**: There are 30 students in total, and 20 are boys, so there are \( 30 - 20 = 10 \) girls. We can find the total marks for the girls by subtracting the total marks of the boys from the total marks of the class. \[ \text{Total marks for girls} = \text{Total marks for class} - \text{Total marks for boys} = 2100 - 1240 = 860. \] 4. **Calculate the mean mark for the girls**: Now we can find the mean mark for the girls by dividing their total marks by the number of girls. \[ \text{Mean mark for girls} = \frac{\text{Total marks for girls}}{\text{Number of girls}} = \frac{860}{10} = 86. \] Therefore, the mean mark for the girls is \( 86\% \).