Understanding the Law College Student Distribution

This problem involves analyzing data from two tables to find a specific value and express it as a percentage of another value. We need to determine the number of students in a particular section and year in College D and compare it to the total number of students in College A.

Step 1: Calculate the Total Number of Students

Table-1 shows the percentage distribution of students across six colleges (A-F). We are given that College C has 1080 students, which represents 20% of the total number of students across all colleges.

Let \(T\) be the total number of students.

According to the information:

\(20\% \text{ of } T = 1080\)

\(\frac{20}{100} \times T = 1080\)

\(0.20 \times T = 1080\)

\(T = \frac{1080}{0.20} = \frac{108000}{20} = 5400\)

So, the total number of students across all six colleges is 5400.

Step 2: Calculate the Number of Students in College A

Table-1 shows that College A has \(8 \frac{1}{3} \%\) of the total students.

First, convert the mixed percentage to a fraction:

\(8 \frac{1}{3} \% = \frac{8 \times 3 + 1}{3} \% = \frac{25}{3} \% = \frac{25}{300} = \frac{1}{12}\)

Number of students in College A = \(T \times \frac{1}{12}\)

Number of students in College A = \(5400 \times \frac{1}{12} = 450\)

Step 3: Calculate the Number of Students in College D

Table-1 shows that College D has \(16 \frac{2}{3} \%\) of the total students.

First, convert the mixed percentage to a fraction:

\(16 \frac{2}{3} \% = \frac{16 \times 3 + 2}{3} \% = \frac{50}{3} \% = \frac{50}{300} = \frac{1}{6}\)

Number of students in College D = \(T \times \frac{1}{6}\)

Number of students in College D = \(5400 \times \frac{1}{6} = 900\)

Step 4: Calculate the Number of Students per Class in College D

The problem states that each of the five classes (1st to 5th year) in College D has the same number of students.

Number of students per class in College D = \(\frac{\text{Total students in College D}}{\text{Number of classes}}\)

Number of students per class in College D = \(\frac{900}{5} = 180\)

So, there are 180 students in each class of College D, including the 4th year class.

Step 5: Calculate the Number of Students in Section III of 4th Year Class in College D

Table-2 provides the section-wise distribution for each class in College D. For the 4th Year class, Section-III has 20% of the students.

Number of students in Section III of 4th year class in College D = \(20\% \text{ of } 180\)

Number of students in Section III of 4th year class in College D = \(\frac{20}{100} \times 180 = 0.20 \times 180 = 36\)

Step 6: Express Students in Section III, 4th Year, College D as a Percentage of Students in College A

We need to find what percentage 36 students (from Section III, 4th Year, College D) is of 450 students (from College A).

Required percentage = \(\frac{\text{Number of students in Section III, 4th Year, College D}}{\text{Number of students in College A}} \times 100\%\)

Required percentage = \(\frac{36}{450} \times 100\%\)

Required percentage = \(\frac{3600}{450}\%\)

Required percentage = \(\frac{360}{45}\%\)

Required percentage = \(8\%\)

The number of students in Section-III of 4th year class in College D is 8% of the total number of students in College A.

Revision Table: Key Calculations Summary

Additional Information: Understanding Percentages and Fractions

Percentages are a way to express a part of a whole as a fraction of 100. Converting percentages to fractions (like \(8 \frac{1}{3} \% = \frac{1}{12}\) and \(16 \frac{2}{3} \% = \frac{1}{6}\)) can simplify calculations, especially when dealing with common fractions like 1/12 and 1/6.

• To convert a percentage to a decimal, divide by 100. E.g., \(20\% = 20/100 = 0.20\).
• To convert a percentage to a fraction, write the percentage over 100 and simplify. E.g., \(20\% = 20/100 = 1/5\).
• Mixed percentages like \(8 \frac{1}{3} \%\) are first converted to an improper fraction (\(\frac{25}{3}\)) and then divided by 100 (\(\frac{25}{300}\)).

Data interpretation problems often require calculating values based on percentages and then finding a percentage relationship between two calculated values. Breaking down the problem into smaller steps helps manage the calculations effectively.