The following table-1 shows the percentage distribution of the number of students studying in six different Law Colleges (A-F) offering a 5-year course and table-2 shows the percentage distribution of the number of students studying in three different Sections I, II and III of each of the five classes (1st to 5th year) for college D. There is a total of 1080 students studying in College C and each class of College D has the same number of students. Based on the data in the tables, answer the question: Table-1: Collage-wise Distribution of Students Table-2 Class-wise & Section-wise distribution (%) of Students for College D Class Section I II III 1st Year 30% 35% 35% 2nd Year 50% 25% 25% 3rd Year 20% 55% 25% 4th Year 45% 35% 20% 5th Year 35% 30% 35%College Distribution (%) of Students A \(8 \frac{1}{3} \%\) B 10% C 20% D \(16 \frac{2}{3} \%\) E 30% F 15%
The number of students in Section-III of 4th year class in College D is ___________ % of the total number of students in College A.
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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.
| Calculation Step | Value | Explanation |
|---|---|---|
| Total Students (T) | 5400 | Calculated from College C data (20% = 1080) |
| Students in College A | 450 | \(8 \frac{1}{3} \%\) of Total Students (5400) |
| Students in College D | 900 | \(16 \frac{2}{3} \%\) of Total Students (5400) |
| Students per class in College D | 180 | Total students in College D (900) divided by 5 classes |
| Students in Section III, 4th Year, College D | 36 | 20% of students in 4th Year Class (180) |
| Required Percentage | 8% | \(\frac{36}{450} \times 100\%\) |
Revision Table: Key Calculations Summary
| Item | Calculation | Result |
|---|---|---|
| Total Students | \(1080 / 0.20\) | 5400 |
| Students in College A | \(5400 \times \frac{1}{12}\) | 450 |
| Students in College D | \(5400 \times \frac{1}{6}\) | 900 |
| Students per class in D | \(900 / 5\) | 180 |
| Students in Sec III, 4th Yr, D | \(180 \times 0.20\) | 36 |
| Percentage | \(\frac{36}{450} \times 100\) | 8% |
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.
Important Questions from Tabulation
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