Analysing College Student Distribution Data

The question asks for the ratio of students studying at PG level to those studying at UG level specifically from college F, based on the provided table and total student numbers. The table gives the percentage distribution of UG and PG students across seven colleges (A-G).

We are given the total number of students in all colleges is 52,000, and the total number of UG students is 27,300.

Calculating Total PG Students

First, we need to find the total number of PG students across all colleges.

Total students = Total UG students + Total PG students

Therefore,

\(\text{Total PG students} = \text{Total students} - \text{Total UG students}\)

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

So, there are 24,700 PG students in total across all colleges.

Finding Students in College F

Now, we need to find the number of UG and PG students specifically in college F.

Number of UG Students in College F

According to the table, 14% of the total UG students are in college F. Total UG students are 27,300.

\(\text{UG students in College F} = 14\% \text{ of } 27,300\)

\(\text{UG students in College F} = \frac{14}{100} \times 27,300\)

\(\text{UG students in College F} = 14 \times 273 = 3822\)

There are 3822 UG students in College F.

Number of PG Students in College F

According to the table, 21% of the total PG students are in college F. Total PG students are 24,700.

\(\text{PG students in College F} = 21\% \text{ of } 24,700\)

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

\(\text{PG students in College F} = 21 \times 247 = 5187\)

There are 5187 PG students in College F.

Determining the Ratio of PG to UG Students in College F

The question asks for the ratio between the number of students studying at PG and UG level respectively from college F. This means we need the ratio PG students : UG students.

\(\text{Ratio (PG : UG) in College F} = \text{Number of PG students in F} : \text{Number of UG students in F}\)

\(\text{Ratio} = 5187 : 3822\)

To simplify this ratio, we can find common factors. Let's divide both numbers by 273:

\(5187 \div 273 = 19\)

\(3822 \div 273 = 14\)

So, the simplified ratio is \(19 : 14\).

Alternatively, we could express the ratio before calculating the final numbers:

\(\text{Ratio} = (21\% \text{ of } 24,700) : (14\% \text{ of } 27,300)\)

\(\text{Ratio} = \left(\frac{21}{100} \times 24,700\right) : \left(\frac{14}{100} \times 27,300\right)\)

Cancel out \(\frac{1}{100}\) from both sides:

\(\text{Ratio} = (21 \times 24,700) : (14 \times 27,300)\)

Divide both sides by 100:

\(\text{Ratio} = (21 \times 247) : (14 \times 273)\)

Factor out common terms (21 = 3x7, 14 = 2x7):

\(\text{Ratio} = (3 \times 7 \times 247) : (2 \times 7 \times 273)\)

Cancel out 7 from both sides:

\(\text{Ratio} = (3 \times 247) : (2 \times 273)\)

Calculate the products:

\(3 \times 247 = 741\)

\(2 \times 273 = 546\)

\(\text{Ratio} = 741 : 546\)

Simplify the ratio \(741 : 546\). Both are divisible by 3 (since sum of digits is divisible by 3):

\(741 \div 3 = 247\)

\(546 \div 3 = 182\)

\(\text{Ratio} = 247 : 182\)

Both 247 and 182 are divisible by 13:

\(247 \div 13 = 19\)

\(182 \div 13 = 14\)

\(\text{Ratio} = 19 : 14\)

Both methods confirm the ratio of PG students to UG students in College F is 19 : 14.

Revision Table: Key Data Points for College F Ratio

Additional Information: Ratio Concepts and Data Interpretation

A ratio is a way to compare two quantities. It shows how many times one quantity is contained within the other or how the two quantities relate to each other. Ratios can be written with a colon (a:b), as a fraction (\(\frac{a}{b}\)), or using the word 'to' (a to b).

Simplifying Ratios: Just like fractions, ratios can be simplified by dividing both parts by their greatest common divisor (GCD).

Percentage Distribution: A percentage distribution shows how a total quantity is divided into categories, with each category's share expressed as a percentage of the total. To find the actual number for a category, you multiply the total by the category's percentage divided by 100.

This question is a typical example of data interpretation from tables, requiring calculation of absolute numbers from percentages and then finding a ratio. Pay close attention to whether the percentage refers to the total population or a sub-population (like total UG or total PG).