Analyzing Student Enrollment Data and Calculating Ratios

The question requires us to calculate the ratio of the total number of students enrolled in the B.C.A. programme in colleges C and E combined to the total number of students enrolled in the B.A. programme in colleges A and B combined, based on the provided table of college-wise enrollment data.

Extracting Data for Ratio Calculation

First, let's identify the number of students for each specific category mentioned in the question from the given table:

• Number of students studying B.C.A. in College C
• Number of students studying B.C.A. in College E
• Number of students studying B.A. in College A
• Number of students studying B.A. in College B

Calculating Total Students for Each Category

Now, we calculate the sums for the two groups mentioned in the ratio:

Total number of students studying B.C.A. in colleges C and E together:

\(\text{Total B.C.A. (C + E)} = \text{Students in B.C.A. (C)} + \text{Students in B.C.A. (E)}\)

\(\text{Total B.C.A. (C + E)} = 300 + 425 = 725\)

Total number of students studying B.A. in colleges A and B together:

\(\text{Total B.A. (A + B)} = \text{Students in B.A. (A)} + \text{Students in B.A. (B)}\)

\(\text{Total B.A. (A + B)} = 275 + 300 = 575\)

Determining the Respective Ratio

The respective ratio of the total number of students studying in B.C.A. in colleges C and E together to those studying in B.A. in colleges A and B together is:

\(\text{Ratio} = \text{Total B.C.A. (C + E)} : \text{Total B.A. (A + B)}\)

\(\text{Ratio} = 725 : 575\)

To simplify the ratio, we find the greatest common divisor (GCD) of 725 and 575. Both numbers end in 5, so they are divisible by 5. Let's divide both by 5:

\(725 \div 5 = 145\)

\(575 \div 5 = 115\)

The ratio becomes \(145 : 115\). Both 145 and 115 end in 5, so they are still divisible by 5. Let's divide both by 5 again:

\(145 \div 5 = 29\)

\(115 \div 5 = 23\)

The simplified ratio is \(29 : 23\).

Since 29 and 23 are prime numbers, the ratio cannot be simplified further.

Therefore, the respective ratio of the total number of students studying in B.C.A. in colleges C and E together to those studying in B.A. in colleges A and B together is 29 : 23.

Revision Table: Key Calculations

Additional Information: Understanding Ratios in Data Analysis

A ratio is a way to compare two or more quantities. It shows the relative size of one value compared to another. In data analysis, ratios are frequently used to understand proportions and make comparisons across different categories or groups.

• Simplifying Ratios: Ratios are typically simplified by dividing all parts of the ratio by their greatest common divisor (GCD). This helps in understanding the relationship in its most basic form.
• Applications: Ratios are used in various fields, such as finance (e.g., profit margins, debt-to-equity), science (e.g., mixture proportions), and demographics (e.g., male-to-female ratio). In educational data, ratios can help compare enrollment trends, resource allocation per student, etc.
• Interpreting Ratios: A ratio like 29:23 means that for every 29 students in the first group, there are 23 students in the second group. It provides a scale to compare the magnitudes of the two numbers.