Understanding the College Student Enrollment Data

The question asks for the ratio of the total number of students enrolled in three specific academic programmes: B.C.A., B.A., and B.B.A., across all five colleges (A, B, C, D, and E). To find this ratio, we first need to calculate the total number of students for each programme by summing the enrollments from all colleges.

Here is the provided table showing the college-wise enrollment data:

Calculating Total Enrollment for Each Programme

We will sum the number of students in each programme across all colleges (A to E).

Total Number of B.A. Students:

Sum of B.A. students in Colleges A, B, C, D, and E:

\( \text{Total B.A.} = 275 + 300 + 325 + 450 + 325 \)

\( \text{Total B.A.} = 1675 \)

Total Number of B.C.A. Students:

Sum of B.C.A. students in Colleges A, B, C, D, and E:

\( \text{Total B.C.A.} = 350 + 325 + 300 + 375 + 425 \)

\( \text{Total B.C.A.} = 1775 \)

Total Number of B.B.A. Students:

Sum of B.B.A. students in Colleges A, B, C, D, and E:

\( \text{Total B.B.A.} = 425 + 475 + 325 + 425 + 225 \)

\( \text{Total B.B.A.} = 1875 \)

Forming and Simplifying the Ratio

The question asks for the ratio of the total number of students studying in B.C.A., B.A., and B.B.A. in all the colleges together. The order specified is B.C.A. : B.A. : B.B.A.

Initial Ratio = Total B.C.A. : Total B.A. : Total B.B.A.

Initial Ratio = \( 1775 : 1675 : 1875 \)

To simplify this ratio, we need to find the greatest common divisor (GCD) of 1775, 1675, and 1875. Since all numbers end in 5, they are divisible by 5.

Divide each number by 5:

• \( 1775 \div 5 = 355 \)
• \( 1675 \div 5 = 335 \)
• \( 1875 \div 5 = 375 \)

The ratio is now \( 355 : 335 : 375 \). All these numbers also end in 5, so they are again divisible by 5.

Divide each number by 5:

• \( 355 \div 5 = 71 \)
• \( 335 \div 5 = 67 \)
• \( 375 \div 5 = 75 \)

The simplified ratio is \( 71 : 67 : 75 \).

We check if these numbers have any common factors other than 1. 71 and 67 are prime numbers. 75 is \( 3 \times 5^2 \). None of these numbers share common factors, so the ratio \( 71 : 67 : 75 \) is in its simplest form.

The respective ratio of total students in B.C.A. : B.A. : B.B.A. is \( 71 : 67 : 75 \).

Conclusion

The calculated ratio of the total number of students in B.C.A., B.A., and B.B.A. programmes across all colleges is \( 71 : 67 : 75 \).

Revision Table: Key Calculations

Additional Information: Data Interpretation and Ratios

Data interpretation questions often require extracting specific information from tables or charts and performing calculations like sums, averages, percentages, or ratios. A ratio is a way to compare two or more quantities. It shows the relative sizes of the quantities. When working with ratios, it's often helpful to simplify them to their lowest terms by dividing all parts of the ratio by their greatest common divisor. Understanding the order in which the ratio is requested (e.g., B.C.A. : B.A. : B.B.A.) is crucial for selecting the correct option.