Finding the Difference Between Boys and Girls in School Classes

The problem provides a table showing the percentage distribution of 600 students across six classes (A-F) and the ratio of boys to girls in each class. We need to calculate the total number of boys and girls across all classes and then find the difference between these totals.

Step 1: Calculate the Number of Students in Each Class

The total number of students in the school is 600. We use the given percentage distribution to find the number of students in each class:

• Class A: \(20\%\) of 600 = \(0.20 \times 600 = 120\) students
• Class B: \(12\%\) of 600 = \(0.12 \times 600 = 72\) students
• Class C: \(16\%\) of 600 = \(0.16 \times 600 = 96\) students
• Class D: \(15\%\) of 600 = \(0.15 \times 600 = 90\) students
• Class E: \(21\%\) of 600 = \(0.21 \times 600 = 126\) students
• Class F: \(16\%\) of 600 = \(0.16 \times 600 = 96\) students

Let's quickly check if the total matches: \(120 + 72 + 96 + 90 + 126 + 96 = 600\). The calculation is correct.

Step 2: Calculate the Number of Boys and Girls in Each Class

For each class, we use the student count and the given ratio of boys to girls to find the number of boys and girls. If the ratio is Boys : Girls, say \(B : G\), the total parts in the ratio are \(B + G\). The number of boys is (Total students in class) \(\times \frac{B}{B+G}\) and the number of girls is (Total students in class) \(\times \frac{G}{B+G}\).

• Class A (120 students, Ratio 3:2): Total parts = \(3+2=5\). Boys = \(120 \times \frac{3}{5} = 72\). Girls = \(120 \times \frac{2}{5} = 48\).
• Class B (72 students, Ratio 3:1): Total parts = \(3+1=4\). Boys = \(72 \times \frac{3}{4} = 54\). Girls = \(72 \times \frac{1}{4} = 18\).
• Class C (96 students, Ratio 5:3): Total parts = \(5+3=8\). Boys = \(96 \times \frac{5}{8} = 60\). Girls = \(96 \times \frac{3}{8} = 36\).
• Class D (90 students, Ratio 8:7): Total parts = \(8+7=15\). Boys = \(90 \times \frac{8}{15} = 48\). Girls = \(90 \times \frac{7}{15} = 42\).
• Class E (126 students, Ratio 4:3): Total parts = \(4+3=7\). Boys = \(126 \times \frac{4}{7} = 72\). Girls = \(126 \times \frac{3}{7} = 54\).
• Class F (96 students, Ratio 1:1): Total parts = \(1+1=2\). Boys = \(96 \times \frac{1}{2} = 48\). Girls = \(96 \times \frac{1}{2} = 48\).

Step 3: Summarize Class-wise Distribution

Here is a table summarizing the number of students, boys, and girls in each class:

Step 4: Calculate Total Number of Boys and Girls

Now, we sum the number of boys and girls from all classes:

• Total Boys = \(72 + 54 + 60 + 48 + 72 + 48 = 354\)
• Total Girls = \(48 + 18 + 36 + 42 + 54 + 48 = 246\)

Step 5: Find the Difference Between Total Boys and Girls

The difference between the total number of boys and total number of girls is:

\(\text{Difference} = |\text{Total Boys} - \text{Total Girls}|\)

\(\text{Difference} = |354 - 246|\)

\(\text{Difference} = 108\)

The difference between the number of boys and girls in all six classes together is 108.

Revision Table: Key Calculations Summary

Additional Information: Understanding Ratios and Percentages

This problem combines the concepts of percentages and ratios. Understanding how to work with these is crucial for solving data interpretation problems like this.

• Percentage: A percentage represents a part of a whole, expressed as a fraction of 100. For example, 20% means 20 out of 100. To find a percentage of a number, convert the percentage to a decimal (divide by 100) and multiply by the number.
• Ratio: A ratio compares two or more quantities. For example, a ratio of 3:2 means that for every 3 units of the first quantity, there are 2 units of the second quantity. The total number of parts in the ratio is the sum of the individual parts (e.g., 3+2=5). To distribute a total quantity according to a ratio, divide the total quantity by the sum of the ratio parts, and then multiply the result by each part of the ratio.

In this problem, we first used percentages to find the number of students in each class based on the total school strength. Then, we used the ratio of boys to girls within each class to distribute the class's student count into boys and girls. Finally, simple arithmetic (addition and subtraction) was used to find the required total counts and their difference.