Understanding the Data Distribution Across Colleges

The provided table gives us the percentage distribution of the total number of students and the total number of girls across six different colleges (A, B, C, D, E, and F). We are also given the total number of students and the total number of girls across all these colleges combined.

• Total number of students in all colleges = 60000
• Total number of girls in all colleges = 24000

We can find the total number of boys across all colleges by subtracting the total number of girls from the total number of students: Total boys = Total students - Total girls Total boys = $60000 - 24000 = 36000$

The table shows the distribution for each college:

Calculating Student and Girl Numbers in Colleges D and F

To find the number of boys in a specific college, we first need to calculate the total number of students and the total number of girls in that college using the given percentages and total numbers. The number of boys in a college is the total students minus the total girls in that college.

Let's calculate for College D and College F, as these are required for the ratio:

• For College D:
  • Total students in College D = 18% of 60000 = $\frac{18}{100} \times 60000 = 18 \times 600 = 10800$
  • Total girls in College D = 14% of 24000 = $\frac{14}{100} \times 24000 = 14 \times 240 = 3360$
• For College F:
  • Total students in College F = 24% of 60000 = $\frac{24}{100} \times 60000 = 24 \times 600 = 14400$
  • Total girls in College F = 21% of 24000 = $\frac{21}{100} \times 24000 = 21 \times 240 = 5040$

Determining the Number of Boys in Colleges D and F

Now, we can find the number of boys in each of these colleges:

• Number of boys in College D = Total students in D - Total girls in D = $10800 - 3360 = 7440$
• Number of boys in College F = Total students in F - Total girls in F = $14400 - 5040 = 9360$

Calculating the Required Ratio of Boys

The question asks for the ratio of the number of boys in College F with the number of boys in College D. Based on the structure of the options provided, we will calculate the ratio of the number of boys in College D to the number of boys in College F.

Ratio = Number of boys in College D : Number of boys in College F

Ratio = $7440 : 9360$

To simplify the ratio, we can divide both numbers by their greatest common divisor or simplify step-by-step:

• Divide both by 10: $744 : 936$
• Divide both by 12: $744 \div 12 = 62$, $936 \div 12 = 78$. The ratio is $62 : 78$.
• Divide both by 2: $62 \div 2 = 31$, $78 \div 2 = 39$. The ratio is $31 : 39$.

Final Answer

The ratio of the number of boys in College D with the number of boys in College F is $31 : 39$.

Revision Table: Key Concepts & Calculations

Additional Information: Percentage Distribution and Ratio Analysis

Understanding percentage distribution is crucial for data interpretation questions. A percentage represents a part out of a hundred. In this case, the percentages show how the total number of students or girls is divided among the different colleges. For example, 18% distribution of students in College D means that 18% of the total 60000 students study in College D.

A ratio is a comparison of two numbers. It shows how much of one quantity there is compared to another quantity. Ratios can be written with a colon (e.g., $31 : 39$) or as a fraction (e.g., $\frac{31}{39}$). Ratios should always be simplified to their lowest terms by dividing both numbers by their greatest common divisor. In our calculation, we simplified the ratio $7440 : 9360$ down to $31 : 39$. Data interpretation questions often require calculating values based on percentages and then finding ratios or differences between these values.