Understanding the School Student Data Distribution

This problem requires us to analyze 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 total students in each class and the ratio of boys to girls within each class. The total number of students in the school is 600. We need to find which pair of classes has an equal number of boys.

Analyzing the Provided School Data Table

The table shows the following information:

Step-by-Step Calculation of Students per Class

First, we need to calculate the total number of students in each class based on the given percentages and the total school strength of 600 students.

• Class A: \( 20\% \text{ of } 600 = \frac{20}{100} \times 600 = 0.20 \times 600 = 120 \text{ students} \)

• Class B: \( 12\% \text{ of } 600 = \frac{12}{100} \times 600 = 0.12 \times 600 = 72 \text{ students} \)

• Class C: \( 16\% \text{ of } 600 = \frac{16}{100} \times 600 = 0.16 \times 600 = 96 \text{ students} \)

• Class D: \( 15\% \text{ of } 600 = \frac{15}{100} \times 600 = 0.15 \times 600 = 90 \text{ students} \)

• Class E: \( 21\% \text{ of } 600 = \frac{21}{100} \times 600 = 0.21 \times 600 = 126 \text{ students} \)

• Class F: \( 16\% \text{ of } 600 = \frac{16}{100} \times 600 = 0.16 \times 600 = 96 \text{ students} \)

Calculating the Number of Boys in Each Class

Next, we will use the boy-to-girl ratio for each class to find the number of boys.

• Class A: Ratio 3:2. Total parts = \( 3+2 = 5 \). Boys = \( \frac{3}{5} \times 120 = 3 \times 24 = 72 \text{ boys} \)

• Class B: Ratio 3:1. Total parts = \( 3+1 = 4 \). Boys = \( \frac{3}{4} \times 72 = 3 \times 18 = 54 \text{ boys} \)

• Class C: Ratio 5:3. Total parts = \( 5+3 = 8 \). Boys = \( \frac{5}{8} \times 96 = 5 \times 12 = 60 \text{ boys} \)

• Class D: Ratio 8:7. Total parts = \( 8+7 = 15 \). Boys = \( \frac{8}{15} \times 90 = 8 \times 6 = 48 \text{ boys} \)

• Class E: Ratio 4:3. Total parts = \( 4+3 = 7 \). Boys = \( \frac{4}{7} \times 126 = 4 \times 18 = 72 \text{ boys} \)

• Class F: Ratio 1:1. Total parts = \( 1+1 = 2 \). Boys = \( \frac{1}{2} \times 96 = 48 \text{ boys} \)

Comparing the Number of Boys Across Classes

Now, let's list the number of boys in each class and compare them to find pairs with an equal number of boys.

• Class A: 72 boys
• Class B: 54 boys
• Class C: 60 boys
• Class D: 48 boys
• Class E: 72 boys
• Class F: 48 boys

By examining the number of boys, we can see that:

• Class A has 72 boys, and Class E has 72 boys.
• Class D has 48 boys, and Class F has 48 boys.

The question asks for a pair of classes from the given options that have an equal number of boys. Let's check the options:

• A and C: 72 boys (A) vs 60 boys (C) - Not equal.
• C and F: 60 boys (C) vs 48 boys (F) - Not equal.
• D and F: 48 boys (D) vs 48 boys (F) - Equal.
• E and F: 72 boys (E) vs 48 boys (F) - Not equal.

Conclusion: Identifying Classes with Equal Boys

Based on our calculations and comparison, the pair of classes with an equal number of boys is Class D and Class F, both having 48 boys.

Revision Table: School Student Data Analysis

Quick summary of calculated values:

Additional Information: Data Interpretation Skills

Data interpretation questions, like this one, are common in many exams. They test your ability to understand and extract information from tables, charts, and graphs, and then perform calculations based on that data. Key skills involved include:

• Reading and understanding data presented in tables.
• Calculating percentages based on a total value.
• Dividing a quantity according to a given ratio.
• Comparing calculated values to draw conclusions or answer specific questions.

Practicing different types of data representation (bar graphs, pie charts, line graphs, tables) and associated calculations (percentages, ratios, averages) is crucial for mastering data interpretation. Always read the question carefully to understand exactly what is being asked.