Understanding the School Student Data

The problem provides a table showing the distribution of students across six classes (A, B, C, D, E, F) in a school. We are given the percentage of the total number of students in each class and the ratio of boys to girls within each class. The total number of students in the school across all six classes is 600. We need to find the average number of girls studying in all six classes.

Calculating the Number of Students in Each Class

First, let's calculate the actual number of students in each class using the given percentages and the total number of students (600).

• Class A: $20\%$ of $600 = \frac{20}{100} \times 600 = 0.20 \times 600 = 120$ students.
• Class B: $12\%$ of $600 = \frac{12}{100} \times 600 = 0.12 \times 600 = 72$ students.
• Class C: $16\%$ of $600 = \frac{16}{100} \times 600 = 0.16 \times 600 = 96$ students.
• Class D: $15\%$ of $600 = \frac{15}{100} \times 600 = 0.15 \times 600 = 90$ students.
• Class E: $21\%$ of $600 = \frac{21}{100} \times 600 = 0.21 \times 600 = 126$ students.
• Class F: $16\%$ of $600 = \frac{16}{100} \times 600 = 0.16 \times 600 = 96$ students.

Determining the Number of Girls in Each Class

Now, using the ratio of boys to girls in each class, we can find the number of girls. The ratio gives us the proportion of boys and girls. The total number of parts in the ratio is the sum of the boy and girl parts. The number of girls is the total students in the class multiplied by the fraction representing girls (girl parts / total parts).

• Class A: Ratio 3:2. Total parts $= 3+2=5$. Number of girls $= \frac{2}{5} \times 120 = 2 \times 24 = 48$.
• Class B: Ratio 3:1. Total parts $= 3+1=4$. Number of girls $= \frac{1}{4} \times 72 = 1 \times 18 = 18$.
• Class C: Ratio 5:3. Total parts $= 5+3=8$. Number of girls $= \frac{3}{8} \times 96 = 3 \times 12 = 36$.
• Class D: Ratio 8:7. Total parts $= 8+7=15$. Number of girls $= \frac{7}{15} \times 90 = 7 \times 6 = 42$.
• Class E: Ratio 4:3. Total parts $= 4+3=7$. Number of girls $= \frac{3}{7} \times 126 = 3 \times 18 = 54$.
• Class F: Ratio 1:1. Total parts $= 1+1=2$. Number of girls $= \frac{1}{2} \times 96 = 1 \times 48 = 48$.

Calculating Total and Average Number of Girls

Next, we find the total number of girls by summing the number of girls from all six classes.

Total number of girls $= \text{Girls in A} + \text{Girls in B} + \text{Girls in C} + \text{Girls in D} + \text{Girls in E} + \text{Girls in F}$

Total number of girls $= 48 + 18 + 36 + 42 + 54 + 48 = 246$.

Finally, to find the average number of girls, we divide the total number of girls by the number of classes, which is 6.

Average number of girls $= \frac{\text{Total number of girls}}{\text{Number of classes}}$

Average number of girls $= \frac{246}{6} = 41$.

Conclusion

The average number of girls studying in all six classes A-F is 41.

Revision Table: Understanding Percentages and Ratios

Additional Information: Data Interpretation Strategies

Interpreting data from tables like this is common in quantitative aptitude problems. Here are some tips:

• Always read the table title and column/row headers carefully to understand what the data represents.
• Identify the total value if percentages are given (like the total of 600 students here).
• Understand how ratios relate to the total quantity they are dividing (e.g., a 3:2 ratio means 3 parts and 2 parts make a total of 5 parts).
• Break down the problem into smaller steps: first find absolute values from percentages, then use ratios to find specific sub-groups.
• Double-check calculations, especially when dealing with multiple steps.