Understanding College Enrollment Data

This problem asks us to determine the total number of boys enrolled in two specific streams, Management and IT, based on the provided college enrollment data for the 2019-20 session. We are given the total number of students, the total number of girls, and the percentage distribution of students and girls across five different streams: IT, Management, Commerce, Science, and Arts.

Analyzing the Provided Enrollment Data

We are given the following key figures:

• Total number of students enrolled: 3500
• Total number of girls enrolled: 1500

From these numbers, we can first find the total number of boys enrolled in the college:

Total Boys = Total Students - Total Girls

\( \text{Total Boys} = 3500 - 1500 = 2000 \)

Now, let's look at the stream-wise enrollment percentages presented in the table:

To find the number of boys in a specific stream, we need to calculate the total number of students in that stream and the total number of girls in that stream, and then subtract the number of girls from the total number of students for that stream.

Calculating Boys Enrollment in IT Stream

For the IT stream:

• Percentage of total students in IT = 20%
• Number of total students in IT = 20% of 3500

\( \text{Number of total students in IT} = \frac{20}{100} \times 3500 = 0.20 \times 3500 = 700 \)

• Percentage of girls in IT = 18%
• Number of girls in IT = 18% of 1500

\( \text{Number of girls in IT} = \frac{18}{100} \times 1500 = 0.18 \times 1500 = 270 \)

Number of boys in IT = Number of total students in IT - Number of girls in IT

\( \text{Number of boys in IT} = 700 - 270 = 430 \)

Calculating Boys Enrollment in Management Stream

For the Management stream:

• Percentage of total students in Management = 16%
• Number of total students in Management = 16% of 3500

\( \text{Number of total students in Management} = \frac{16}{100} \times 3500 = 0.16 \times 3500 = 560 \)

• Percentage of girls in Management = 12%
• Number of girls in Management = 12% of 1500

\( \text{Number of girls in Management} = \frac{12}{100} \times 1500 = 0.12 \times 1500 = 180 \)

Number of boys in Management = Number of total students in Management - Number of girls in Management

\( \text{Number of boys in Management} = 560 - 180 = 380 \)

Total Boys in Management and IT Streams

Finally, to find the total number of boys enrolled in Management stream and IT stream together, we add the number of boys from each stream:

Total boys in Management and IT = Boys in IT + Boys in Management

\( \text{Total boys in Management and IT} = 430 + 380 = 810 \)

The total number of boys enrolled in the Management stream and IT stream together is 810.

Revision Table: College Enrollment Calculations

Total Boys in IT and Management = Boys in IT + Boys in Management = \( 430 + 380 = 810 \)

Additional Information: Percentage Calculations and Data Interpretation

When working with percentages from different base values (like percentage of total students and percentage of girls), it is crucial to calculate the absolute numbers for each category before performing additions or subtractions. In this problem, the percentage of students is out of 3500, while the percentage of girls is out of 1500. Simply adding or subtracting percentages directly would lead to an incorrect result.

To find the number of boys in a stream, you subtract the number of girls in that stream from the total number of students in that stream. This approach requires careful calculation of the actual count (not just the percentage) for both categories based on their respective totals.

Understanding how to calculate percentages and apply them to real-world data sets like enrollment figures is a common type of problem in data interpretation and quantitative aptitude questions.