Analyzing Student Distribution and Ratios

The question provides a table showing the distribution of 600 students across six classes (A to F) and the ratio of boys to girls in each class. We need to calculate the difference between the number of boys and girls in two specific classes, A and C, and then find what percentage the difference in class A (P) is of the difference in class C (Q).

Total number of students in the school is 600.

Calculating Students in Class A

First, let's find the total number of students in class A.

• Percentage of students in Class A = 20%
• Total students = 600
• Number of students in Class A = $20\%$ of $600$
• Number of students in Class A = $\frac{20}{100} \times 600 = 0.20 \times 600 = 120$

Calculating Boys and Girls in Class A

The ratio of boys to girls in Class A is 3 : 2.

• Total ratio parts = $3 + 2 = 5$
• Number of boys in Class A = $\frac{\text{Boys ratio part}}{\text{Total ratio parts}} \times \text{Total students in Class A}$
• Number of boys in Class A = $\frac{3}{5} \times 120 = 3 \times \frac{120}{5} = 3 \times 24 = 72$
• Number of girls in Class A = $\frac{\text{Girls ratio part}}{\text{Total ratio parts}} \times \text{Total students in Class A}$
• Number of girls in Class A = $\frac{2}{5} \times 120 = 2 \times \frac{120}{5} = 2 \times 24 = 48$
• Check: $72 + 48 = 120$ (Total students in Class A)

Calculating Difference P in Class A

P is the difference between the number of boys and girls in class A.

• P = Number of boys in Class A - Number of girls in Class A
• P = $72 - 48 = 24$

Calculating Students in Class C

Next, let's find the total number of students in class C.

• Percentage of students in Class C = 16%
• Total students = 600
• Number of students in Class C = $16\%$ of $600$
• Number of students in Class C = $\frac{16}{100} \times 600 = 0.16 \times 600 = 96$

Calculating Boys and Girls in Class C

The ratio of boys to girls in Class C is 5 : 3.

• Total ratio parts = $5 + 3 = 8$
• Number of boys in Class C = $\frac{\text{Boys ratio part}}{\text{Total ratio parts}} \times \text{Total students in Class C}$
• Number of boys in Class C = $\frac{5}{8} \times 96 = 5 \times \frac{96}{8} = 5 \times 12 = 60$
• Number of girls in Class C = $\frac{\text{Girls ratio part}}{\text{Total ratio parts}} \times \text{Total students in Class C}$
• Number of girls in Class C = $\frac{3}{8} \times 96 = 3 \times \frac{96}{8} = 3 \times 12 = 36$
• Check: $60 + 36 = 96$ (Total students in Class C)

Calculating Difference Q in Class C

Q is the difference between the number of boys and girls in class C.

• Q = Number of boys in Class C - Number of girls in Class C
• Q = $60 - 36 = 24$

Calculating Percentage of P with Reference to Q

We need to find the percentage of P with reference to Q. This is calculated as $(\frac{P}{Q} \times 100)$.

• P = 24
• Q = 24
• Percentage = $\frac{P}{Q} \times 100 = \frac{24}{24} \times 100 = 1 \times 100 = 100\%$

The percentage of P with reference to Q is 100%.

Revision Table: Key Calculations Summary

Percentage of P with reference to Q = $(\frac{24}{24}) \times 100 = 100\%$.

Additional Information: Percentage and Ratio Concepts

Understanding percentages and ratios is fundamental for solving problems like this one, often found in data interpretation questions.

• Percentage: A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviation "pct.". For example, 20% means 20 out of 100. To find a percentage of a number, you convert the percentage to a decimal (divide by 100) and multiply by the number.
• Ratio: A ratio compares two quantities of the same kind. It is often written with a colon (:) between the quantities, like 3:2. The parts of the ratio represent proportional divisions of a whole. If the ratio of boys to girls is 3:2, it means that for every 3 boys, there are 2 girls. The total number of parts is 3 + 2 = 5. If there are 120 students, each part represents $120/5 = 24$ students. So, boys = $3 \times 24 = 72$ and girls = $2 \times 24 = 48$.
• Percentage 'With Reference To': When you calculate the percentage of one value (X) with reference to another value (Y), you are finding what fraction X is of Y and expressing that fraction as a percentage. The formula is $(\frac{X}{Y}) \times 100\%$.

These concepts are widely applicable in various data analysis scenarios, including student demographics, sales figures, and survey results.