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%
What is the total number of students in Section-I of all classes in College D?
324
Understanding College Student Distribution Data
This problem requires us to analyze data from two tables to find the total number of students in a specific section across all classes in one particular college (College D). We are given percentage distributions of students across colleges and within one college (College D) by class and section. We are also given the total number of students in College C and told that each class in College D has an equal number of students.
Analyzing the Provided Data Tables
Let's first look at the data presented in the tables:
| Table-1: College-wise Distribution of Students | |
|---|---|
| College | Distribution (%) of Students |
| A | \(8 \frac{1}{3} \%\) |
| B | 10% |
| C | 20% |
| D | \(16 \frac{2}{3} \%\) |
| E | 30% |
| F | 15% |
| Table-2 Class-wise & Section-wise distribution (%) of Students for College D | |||
|---|---|---|---|
| Class | Section I | Section II | Section 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% |
Step-by-Step Calculation of Students in College D Section-I
We need to find the total number of students in Section-I across all five classes in College D. To do this, we first need to find the total number of students in College D, and then the number of students in each class, and finally the number of students in Section-I for each class.
Step 1: Find the Total Number of Students Across All Colleges
We are given that there are 1080 students in College C, which represents 20% of the total students across all six colleges. Let the total number of students be \(T\).
\(20\% \text{ of } T = 1080\)
\(\frac{20}{100} \times T = 1080\)
\(T = \frac{1080 \times 100}{20}\)
\(T = 54 \times 100\)
\(T = 5400\)
So, the total number of students studying in all six colleges is 5400.
Step 2: Find the Total Number of Students in College D
According to Table-1, College D has \(16 \frac{2}{3} \%\) of the total students. \(16 \frac{2}{3} \% = \frac{16 \times 3 + 2}{3} \% = \frac{48 + 2}{3} \% = \frac{50}{3} \%\)
Number of students in College D = \(\frac{50}{3} \% \text{ of } 5400\)
Number of students in College D = \(\frac{50}{3 \times 100} \times 5400\)
Number of students in College D = \(\frac{50}{300} \times 5400\)
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 3: Find the Number of Students in Each Class Year 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 classes = 5 Total students in College D = 900
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 year (1st, 2nd, 3rd, 4th, and 5th year) in College D has 180 students.
Step 4: Find the Number of Students in Section-I for Each Class Year
Now, using Table-2 and the fact that each class has 180 students, we can find the number of students in Section-I for each class.
- 1st Year Section-I: 30% of 180 = \(\frac{30}{100} \times 180 = 0.30 \times 180 = 54\) students
- 2nd Year Section-I: 50% of 180 = \(\frac{50}{100} \times 180 = 0.50 \times 180 = 90\) students
- 3rd Year Section-I: 20% of 180 = \(\frac{20}{100} \times 180 = 0.20 \times 180 = 36\) students
- 4th Year Section-I: 45% of 180 = \(\frac{45}{100} \times 180 = 0.45 \times 180 = 81\) students
- 5th Year Section-I: 35% of 180 = \(\frac{35}{100} \times 180 = 0.35 \times 180 = 63\) students
Step 5: Calculate the Total Number of Students in Section-I Across All Classes in College D
To find the total number of students in Section-I of all classes in College D, we sum the number of students in Section-I from each class year.
Total Section-I students = (1st Year Section-I) + (2nd Year Section-I) + (3rd Year Section-I) + (4th Year Section-I) + (5th Year Section-I)
Total Section-I students = \(54 + 90 + 36 + 81 + 63\)
Total Section-I students = \(144 + 36 + 81 + 63\)
Total Section-I students = \(180 + 81 + 63\)
Total Section-I students = \(261 + 63\)
Total Section-I students = \(324\)
Conclusion
The total number of students in Section-I of all classes in College D is 324.
Revision Table: Key Calculations
| Calculation Step | Details | Result |
|---|---|---|
| Total Students | (Students in C / % of C) * 100 | 5400 |
| Students in College D | Total Students * % of D | 900 |
| Students per Class in D | Total D Students / 5 | 180 |
| 1st Year Section I | 180 * 30% | 54 |
| 2nd Year Section I | 180 * 50% | 90 |
| 3rd Year Section I | 180 * 20% | 36 |
| 4th Year Section I | 180 * 45% | 81 |
| 5th Year Section I | 180 * 35% | 63 |
| Total Section I in D | Sum of Section I per class | 324 |
Additional Information: Data Interpretation Skills
Solving data interpretation problems like this one requires careful reading and step-by-step analysis. Here are some key skills used:
- Understanding Percentages: Knowing how to calculate a percentage of a number and how to find a total when a percentage of it is given.
- Reading Tables: Extracting specific information accurately from rows and columns in different tables.
- Breaking Down the Problem: Dividing a complex question into smaller, manageable steps.
- Sequential Calculation: Using the result of one step as input for the next step.
- Summation: Adding up numbers to find a total quantity.
These problems often involve multiple layers of percentages or distributions, so it's important to track which total or sub-total you are working with at each stage. Paying close attention to the labels in the tables and the conditions given in the question (like "each class ... has the same number of students") is crucial for accuracy.
Important Questions from Tabulation
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