Analysing Student Distribution in Law Colleges

The problem provides data on the percentage distribution of students across six different Law Colleges (A-F) and a detailed class-wise and section-wise distribution specifically for College D. We are given the total number of students in College C and asked about the number of students in a specific section and class of College E after a hypothetical student transfer from College A to College D.

Understanding the Given Data Tables

We have two main sources of information:

1. Table-1: This table shows the percentage of the total number of students studying in each of the six colleges (A, B, C, D, E, F). The percentages add up to 100%.
2. Table-2: This table provides a detailed breakdown for College D only. It shows how the students within College D are distributed percentage-wise across five different classes (1st to 5th year) and three sections (I, II, and III) within each class.

We are also told that there is a total of 1080 students in College C and that each class in College D has the same number of students.

Calculating Total Students and College-wise Numbers

First, let's determine the total number of students across all colleges. We know that College C has 20% of the total students, and this number is 1080.

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

\(20\%\) of \(T = 1080\)

\(0.20 \times T = 1080\)

\(T = \frac{1080}{0.20} = \frac{1080}{\frac{20}{100}} = 1080 \times \frac{100}{20} = 1080 \times 5 = 5400\)

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

Now we can calculate the number of students in each college using the percentages from Table-1:

• College A: \(8 \frac{1}{3}\% = \frac{25}{3}\% = \frac{25}{300} = \frac{1}{12}\) of \(5400 = \frac{1}{12} \times 5400 = 450\) students.
• College B: \(10\%\) of \(5400 = 0.10 \times 5400 = 540\) students.
• College C: \(20\%\) of \(5400 = 0.20 \times 5400 = 1080\) students (as given).
• College D: \(16 \frac{2}{3}\% = \frac{50}{3}\% = \frac{50}{300} = \frac{1}{6}\) of \(5400 = \frac{1}{6} \times 5400 = 900\) students.
• College E: \(30\%\) of \(5400 = 0.30 \times 5400 = 1620\) students.
• College F: \(15\%\) of \(5400 = 0.15 \times 5400 = 810\) students.

Let's summarize the student numbers per college:

Examining Student Transfer from College A to College D

The problem states that 20% of the students in College A move to College D. The number of students in College A is 450.

Students moving from College A = \(20\%\) of \(450 = 0.20 \times 450 = 90\) students.

These 90 students are equally distributed in each class of College D. College D has 5 classes (1st year to 5th year). So, each class in College D receives \(90 / 5 = 18\) additional students.

The total number of students in College A decreases by 90 (\(450 - 90 = 360\)). The total number of students in College D increases by 90 (\(900 + 90 = 990\)). The total number of students across all colleges remains 5400.

Identifying the Required Information for College E

The question asks for the number of students in Section-II of College E's 3rd year class.

We know the total number of students in College E is 1620. The student transfer affects only Colleges A and D, not College E. So, the total number of students in College E remains 1620.

To find the number of students in Section-II of College E's 3rd year class, we would need the following information:

1. The number of students in the 3rd year class within College E.
2. The percentage distribution of students into Section-II within the 3rd year class of College E.

Why the Number Cannot Be Determined

The provided Table-2 gives the class-wise and section-wise distribution of students, but it is explicitly stated as being "for College D" only. There is no information provided in either table about the class-wise or section-wise distribution of students within College E.

Without knowing what percentage of College E students are in the 3rd year class, or how students within College E's 3rd year class are distributed into sections (I, II, and III), it is impossible to calculate the number of students in Section-II of College E's 3rd year class.

The information about the student transfer between College A and College D, and the equal distribution of students within College D's classes, is irrelevant to finding the number of students in College E.

Therefore, based on the data given, the number of students in Section-II of College E's 3rd year class cannot be determined.

Conclusion

The necessary data regarding the internal distribution of students within College E (by class and section) is not provided. Thus, the number of students in Section-II of College E's 3rd year class cannot be calculated.

Revision Table: Key Calculations

Additional Information: Data Interpretation Concepts

Data interpretation questions often require you to extract, calculate, and synthesize information from tables, charts, or graphs. Key concepts involved include:

• Percentages: Understanding how to calculate a percentage of a total, find a total based on a percentage, and work with percentage distributions.
• Ratios and Proportions: Comparing quantities and understanding proportional relationships.
• Data Extraction: Carefully reading the tables and question to identify the relevant numbers and conditions.
• Logical Reasoning: Determining what information is needed to answer the question and assessing whether that information is available. Sometimes, extra information is given that is not required to solve the specific question, or crucial information might be missing, leading to the answer "Cannot be determined".
• Careful Reading: Paying close attention to details, such as which college or category a specific table or piece of information applies to. In this problem, recognizing that Table-2 is only for College D is crucial.

When encountering "Cannot be determined" as an option, always check if there is any missing piece of information that is essential for solving the problem, regardless of how much calculation you can do with the available data.