Understanding Student Enrollment Data

The problem provides a table showing the distribution of student enrollment in a college across five different streams: IT, Management, Commerce, Science, and Arts during the 2019-20 session. We are given the total number of students and the total number of girls enrolled. The question asks us to find what percentage the number of girls enrolled in Arts, Science, and Commerce streams combined represents of the total number of students in the college.

Let's break down the given information:

• Total number of students in the college = 3500
• Total number of girls enrolled in the college = 1500

The table shows the percentage of students enrolled in each stream (out of 3500 total students) and the percentage of girls enrolled in each stream (out of 1500 total girls).

Calculating the Number of Girls in Specific Streams

We need to find the total number of girls enrolled in Arts, Science, and Commerce streams. We can do this by using the percentage of girls enrolled in each of these streams and the total number of girls (1500).

• Girls in Arts: The table shows that 38% of the girls are enrolled in Arts. Total girls in Arts = 38% of 1500 $$= \frac{38}{100} \times 1500$$ $$= 0.38 \times 1500 = 570$$
• Girls in Science: The table shows that 11% of the girls are enrolled in Science. Total girls in Science = 11% of 1500 $$= \frac{11}{100} \times 1500$$ $$= 0.11 \times 1500 = 165$$
• Girls in Commerce: The table shows that 21% of the girls are enrolled in Commerce. Total girls in Commerce = 21% of 1500 $$= \frac{21}{100} \times 1500$$ $$= 0.21 \times 1500 = 315$$

Now, let's find the total number of girls enrolled in Arts, Science, and Commerce streams together:

Total girls (Arts + Science + Commerce) = Girls in Arts + Girls in Science + Girls in Commerce $$= 570 + 165 + 315$$ $$= 1050$$

Finding the Percentage of Total Students

The question asks what percentage the number of girls enrolled in Arts, Science, and Commerce streams together forms of the total number of students in the college.

• Total number of girls in Arts, Science, and Commerce = 1050
• Total number of students in the college = 3500

Percentage = $\left( \frac{\text{Total girls in Arts, Science, and Commerce}}{\text{Total number of students}} \right) \times 100\%$

Percentage = $\left( \frac{1050}{3500} \right) \times 100\%$

We can simplify the fraction: $$ \frac{1050}{3500} = \frac{105}{350} $$ Both 105 and 350 are divisible by 5: $$ \frac{105 \div 5}{350 \div 5} = \frac{21}{70} $$ Both 21 and 70 are divisible by 7: $$ \frac{21 \div 7}{70 \div 7} = \frac{3}{10} $$

Now substitute this back into the percentage calculation: Percentage = $\left( \frac{3}{10} \right) \times 100\%$ $$= 0.3 \times 100\% = 30\%$$

So, the number of girls enrolled in Arts, Science, and Commerce streams together forms 30% of the total number of students in the college.

Revision Table: Key Calculations for Enrollment Percentage

Additional Information: Working with Percentages in Data Analysis

When working with data presented in percentages, it is crucial to understand what the percentage is "of". In this problem, we had two different bases for percentages: the total number of students (3500) for overall stream enrollment and the total number of girls (1500) for girl-specific stream enrollment.

Key concepts include:

• Percentage Calculation: A percentage is a fraction of 100. To find the value of a percentage of a total, you multiply the total by the percentage divided by 100. For example, X% of Y is $ (X/100) \times Y $.
• Identifying the Base: Always check what the percentage is calculated from. In this case, the percentage of girls per stream is out of the total number of girls (1500), not out of the total number of students (3500).
• Combining Data: To find the total number for a group (like girls in Arts, Science, Commerce), calculate the absolute number for each subgroup first, and then add them up. You cannot simply add percentages if they are based on different totals. For example, adding 38% (Arts girls) + 11% (Science girls) + 21% (Commerce girls) = 70% does not directly tell you the percentage of *total students* unless you perform further calculations based on the actual numbers.
• Final Percentage Calculation: The final percentage required was based on the *total number of students* (3500), even though we calculated the number of girls using the total number of girls (1500). This requires careful attention to the denominator in the final percentage formula.

These steps ensure accurate calculation and interpretation of data from tables involving multiple percentage distributions.