Analyzing College Student Distribution Data

The problem asks us to find the ratio between the number of students studying at the PG level from College F and the number of students studying at the UG level from College D, based on the provided table and total student numbers.

Understanding the Given Data

We are given the following key pieces of information:

• Total number of students in all colleges: 52,000
• Total number of UG students in all colleges: 27,300
• The percentage distribution of UG students across colleges A-G.
• The percentage distribution of PG students across colleges A-G.

The table shows the percentage of UG students within the total UG population and the percentage of PG students within the total PG population for each college.

Calculating Total PG Students

First, we need to find the total number of PG students. This can be done by subtracting the total UG students from the total number of students.

Total PG students = Total students - Total UG students

\( \text{Total PG students} = 52,000 - 27,300 = 24,700 \)

Calculating UG Students in College D

The table states that 13% of the UG students are in College D. We use the total number of UG students to find the actual number.

Number of UG students in College D = 13% of Total UG students

\( \text{Number of UG students in College D} = \frac{13}{100} \times 27,300 \)

\( \text{Number of UG students in College D} = 13 \times 273 \)

\( \text{Number of UG students in College D} = 3,549 \)

Calculating PG Students in College F

The table states that 21% of the PG students are in College F. We use the total number of PG students calculated earlier to find the actual number.

Number of PG students in College F = 21% of Total PG students

\( \text{Number of PG students in College F} = \frac{21}{100} \times 24,700 \)

\( \text{Number of PG students in College F} = 21 \times 247 \)

\( \text{Number of PG students in College F} = 5,187 \)

Determining the Ratio

We need to find the ratio between the number of PG students in College F and the number of UG students in College D.

Ratio = (Number of PG students in College F) : (Number of UG students in College D)

Ratio = \( 5,187 : 3,549 \)

To simplify this ratio, we can express the numbers based on their percentage calculations before multiplying fully, as it might reveal common factors:

\( \left( \frac{21}{100} \times 24,700 \right) : \left( \frac{13}{100} \times 27,300 \right) \)

We can multiply both sides by 100 to remove the denominator:

\( (21 \times 24,700) : (13 \times 27,300) \)

Divide both sides by 100:

\( (21 \times 247) : (13 \times 273) \)

Now, let's find common factors for 247 and 273. We can check if 247 is divisible by 13: \( 247 \div 13 = 19 \). So, \( 247 = 13 \times 19 \). We can check if 273 is divisible by 21: \( 273 \div 21 = 13 \). So, \( 273 = 21 \times 13 \).

Substitute these factors back into the ratio:

\( (21 \times 13 \times 19) : (13 \times 21 \times 13) \)

Cancel out the common factors \( 21 \) and \( 13 \) from both sides:

\( 19 : 13 \)

The ratio between the number of students studying at PG level from College F and the number of students studying at UG level from College D is 19 : 13.

Revision Table: College Student Data Ratio

Additional Information on Data Interpretation and Ratios

Data interpretation questions often involve extracting information from tables or charts and performing calculations like percentages, averages, and ratios. Understanding how to work with percentages of given totals is crucial.

• Percentages: A percentage represents a part of a whole, expressed as a fraction of 100. To find a percentage of a number, convert the percentage to a decimal or fraction and multiply by the number. For example, 13% of 27,300 is \( \frac{13}{100} \times 27,300 \).
• Ratios: A ratio is a comparison of two quantities. It shows how many times one quantity is contained within another. Ratios can be written as \( a:b \) or \( \frac{a}{b} \). Ratios should be simplified to their lowest terms by dividing both parts by their greatest common divisor. In this case, we found the ratio of PG students in College F to UG students in College D and simplified it.
• Data Analysis Steps: Typically, solving data interpretation problems involves:
  1. Reading the question carefully to understand what is being asked.
  2. Identifying the relevant data points in the table or chart.
  3. Performing the necessary calculations (percentage, ratio, sum, average, etc.).
  4. Simplifying or comparing the results as required by the question.

This question combined percentage calculation with ratio calculation, a common approach in data interpretation problems.