Analyzing Law College Student Data

The problem requires us to analyze data from two tables showing student distribution in different law colleges and within classes/sections of one specific college (College D). We are given information about the total number of students in College C and a condition relating student numbers in College B and College D.

Let's break down the problem step-by-step:

Step 1: Determine the Total Number of Students

Table 1 provides the percentage distribution of students across six law colleges (A to F). We are given that College C has 1080 students and represents 20% of the total students.

Let $T$ be the total number of students across all six colleges.

From the data:

$20\%$ of $T = 1080$

$\frac{20}{100} \times T = 1080$

$0.2 \times T = 1080$

$T = \frac{1080}{0.2} = \frac{10800}{2} = 5400$

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

Step 2: Calculate the Number of Students in College D

According to Table 1, College D has $16 \frac{2}{3} \%$ of the total students.

$16 \frac{2}{3} \% = \frac{16 \times 3 + 2}{3} \% = \frac{50}{3} \%$

Number of students in College D = $\frac{50}{3} \%$ of Total students

Number of students in College D = $\frac{\frac{50}{3}}{100} \times 5400 = \frac{50}{300} \times 5400 = \frac{1}{6} \times 5400 = 900$

There are 900 students in College D.

Step 3: Calculate the Number of Students Per Class in College D

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

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 = $\frac{900}{5} = 180$

Each class in College D has 180 students.

Step 4: Calculate Students in Section-I of College D's 3rd Year

Table 2 shows the class-wise and section-wise distribution for College D. For the 3rd year class, Section-I has 20% of the students in that class.

Students in 3rd Year (College D) = 180

Students in Section-I of College D's 3rd year = $20\%$ of 180

Students in Section-I of College D's 3rd year = $\frac{20}{100} \times 180 = 0.20 \times 180 = 36$

Step 5: Use the Condition to Find Students in College B

The problem states that Section-II in College B's 2nd year class has the same number of students as Section-I in College D's 3rd year class.

Students in Section-II in College B's 2nd year class = Students in Section-I in College D's 3rd year class = 36.

Step 6: Calculate Students in Section-III of College D's 5th Year

We need to find the number of students in Section-III of College D's 5th year class to form the ratio. From Table 2, for the 5th year class, Section-III has 35% of the students in that class.

Students in 5th Year (College D) = 180

Students in Section-III of College D's 5th year = $35\%$ of 180

Students in Section-III of College D's 5th year = $\frac{35}{100} \times 180 = 0.35 \times 180 = 63$

Step 7: Determine the Required Ratio

We need the ratio of the number of students in Section-II in College B's 2nd year class to that of Section-III in College D's 5th year class.

Ratio = (Students in Section-II in College B's 2nd year class) : (Students in Section-III in College D's 5th year class)

Ratio = 36 : 63

To simplify the ratio, we find the greatest common divisor (GCD) of 36 and 63. The GCD is 9.

Divide both parts of the ratio by 9:

Ratio = $\frac{36}{9} : \frac{63}{9} = 4 : 7$

The ratio of the number of students is $4 \ratio 7$.

Let's summarize the calculated values:

• Total students across all colleges: 5400
• Total students in College D: 900
• Students per class in College D: 180
• Students in Section-I, 3rd Year, College D: 36
• Students in Section-II, 2nd Year, College B: 36 (given condition)
• Students in Section-III, 5th Year, College D: 63
• Required Ratio (College B Sec-II 2nd Year : College D Sec-III 5th Year): 36 : 63 = 4 : 7

Revision Table: Key Data Points and Calculations

Additional Information: Understanding Percentage and Ratio Problems

This problem combines concepts of percentages and ratios, common in data interpretation questions. Understanding how to work with percentage distributions and convert percentages to absolute numbers is crucial. Similarly, knowing how to express relationships between quantities as ratios and simplify them to their lowest terms is important.

• Percentage: A percentage is a fraction of 100. For example, 20% means 20 out of 100, or $\frac{20}{100}$. To find a percentage of a number, convert the percentage to a decimal or fraction and multiply by the number.
• Ratio: A ratio is a comparison of two quantities. It shows how much of one quantity there is compared to another. Ratios can be written with a colon (e.g., a : b) or as a fraction (e.g., $\frac{a}{b}$). Ratios should usually be simplified to their lowest terms by dividing both parts by their greatest common divisor.
• Data Tables: Carefully read and understand the information provided in each table. Pay attention to what each table represents (e.g., overall distribution vs. distribution within a specific category).
• Conditional Information: Some problems provide specific conditions (like the number of students being equal in two different groups) that are necessary to link information from different parts of the problem or different tables.

Solving such problems requires careful reading, accurate calculation, and logical step-by-step reasoning to connect all the given pieces of information.