Analyzing Law College Student Distribution for Data Interpretation

This problem requires us to analyze data presented in two tables related to student distribution in law colleges and within a specific college (College D).

Understanding the Data Tables

We are given two tables:

Table-1 shows the percentage of total students studying in each of the six Law Colleges (A-F).

Table-2 shows the percentage distribution of students within College D across three sections (I, II, III) for each of the five classes (1st to 5th year).

Goal of the Question

The question asks for the difference between the total number of students in College C and the total number of students in Section-III across all classes (1st to 5th year) specifically in College D.

Step-by-Step Solution for Student Distribution

Step 1: Calculate the Total Number of Students Across All Colleges

We are given that there are 1080 students in College C, and from Table-1, College C represents 20% of the total students. We can use this information to find the total number of students.

• Let the total number of students across all colleges be \(T\).
• Percentage of students in College C = 20%
• Number of students in College C = 1080
• So, \(20\% \text{ of } T = 1080\)
• \(\frac{20}{100} \times T = 1080\)
• \(T = \frac{1080 \times 100}{20}\)
• \(T = 1080 \times 5\)
• \(T = 5400\)

The total number of students across all six law colleges is 5400.

Step 2: Determine the Number of Students in College C

The question directly states that there are 1080 students studying in College C.

• Number of students in College C = 1080.

Step 3: Calculate the Total Number of Students in College D

From Table-1, College D has \(16 \frac{2}{3} \%\) of the total students. We need to calculate this percentage of the total students (5400).

• Percentage of students in College D = \(16 \frac{2}{3} \% = \frac{16 \times 3 + 2}{3} \% = \frac{50}{3} \%\)
• As a fraction, \(\frac{50}{3} \% = \frac{50}{3 \times 100} = \frac{50}{300} = \frac{1}{6}\)
• Number of students in College D = \(\frac{1}{6} \times \text{Total Students}\)
• Number of students in College D = \(\frac{1}{6} \times 5400\)
• Number of students in College D = 900

There are 900 students in College D.

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

We are told that each of the five classes (1st to 5th year) in College D has the same number of students.

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

Each class in College D has 180 students.

Step 5: Calculate the Number of Students in Section-III for Each Class in College D

Using Table-2 and the number of students per class (180), we can find the number of students in Section-III for each year.

• 1st Year, Section III: 35% of 180 = \(0.35 \times 180 = 63\) students
• 2nd Year, Section III: 25% of 180 = \(0.25 \times 180 = 45\) students
• 3rd Year, Section III: 25% of 180 = \(0.25 \times 180 = 45\) students
• 4th Year, Section III: 20% of 180 = \(0.20 \times 180 = 36\) students
• 5th Year, Section III: 35% of 180 = \(0.35 \times 180 = 63\) students

Step 6: Calculate the Total Number of Students in Section-III Across All Classes in College D

Sum the number of students in Section-III for each class calculated in Step 5.

• Total students in Section-III (College D) = Students in 1st Year (Sec III) + 2nd Year (Sec III) + 3rd Year (Sec III) + 4th Year (Sec III) + 5th Year (Sec III)
• Total students in Section-III (College D) = \(63 + 45 + 45 + 36 + 63\)
• Total students in Section-III (College D) = 252 students

Step 7: Calculate the Difference

The question asks for the difference between the number of students in College C and the total number of students in Section-III across all classes in College D.

• Difference = Number of students in College C - Total students in Section-III (College D)
• Difference = \(1080 - 252\)
• Difference = 828

The difference between the number of students in College C and in Section-III across all classes in College D is 828.

Revision Table: Key Calculations

Additional Information on Percentage Distribution

Data interpretation often involves understanding and calculating with percentages. A percentage is a number or ratio expressed as a fraction of 100. Converting percentages to decimals or fractions is crucial for calculations.

• To convert a percentage to a decimal, divide by 100. For example, 20% = \(20/100 = 0.20\).
• To convert a percentage to a fraction, write the percentage over 100 and simplify. For example, \(20\% = \frac{20}{100} = \frac{1}{5}\).
• Mixed number percentages like \(16 \frac{2}{3} \%\) should first be converted to an improper fraction (\(\frac{50}{3}\)) before dividing by 100 to get the fractional or decimal equivalent.
• When dealing with distribution tables, ensure the percentages for a whole category (like colleges in Table-1 or sections within a class in Table-2) sum up to 100%. (Note: Table-2 percentages per row sum to 100%).

Understanding how to extract specific data points and perform calculations based on given conditions (like "each class of College D has the same number of students") is key to solving these types of quantitative problems.