Understanding the Student Enrollment Data

The problem provides a table showing the distribution of student enrollment across five different streams in a college during the 2019-20 session. We are given the total number of students and the total number of girls enrolled. The table provides percentages for both total students and girls enrolled per stream.

Total Students = 3500

Total Girls = 1500

From this, we can find the total number of boys:

Total Boys = Total Students - Total Girls

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

Calculating the Number of Girls in Arts

We need to find the number of girls enrolled specifically in the Arts stream. The table states that 38% of the total girls are enrolled in Arts.

Number of girls in Arts = 38% of Total Girls

\( \text{Number of girls in Arts} = \frac{38}{100} \times 1500 \)

\( \text{Number of girls in Arts} = 0.38 \times 1500 \)

\( \text{Number of girls in Arts} = 570 \)

Calculating the Number of Boys in Science

To find the number of boys in the Science stream, we first need to find the total number of students in Science and the number of girls in Science. The difference will give us the number of boys.

Step 1: Find Total Students in Science

The table shows that 22% of the total students are enrolled in Science.

Number of students in Science = 22% of Total Students

\( \text{Number of students in Science} = \frac{22}{100} \times 3500 \)

\( \text{Number of students in Science} = 0.22 \times 3500 \)

\( \text{Number of students in Science} = 770 \)

Step 2: Find Number of Girls in Science

The table shows that 11% of the total girls are enrolled in Science.

Number of girls in Science = 11% of Total Girls

\( \text{Number of girls in Science} = \frac{11}{100} \times 1500 \)

\( \text{Number of girls in Science} = 0.11 \times 1500 \)

\( \text{Number of girls in Science} = 165 \)

Step 3: Find Number of Boys in Science

Number of boys in Science = Total Students in Science - Number of girls in Science

\( \text{Number of boys in Science} = 770 - 165 \)

\( \text{Number of boys in Science} = 605 \)

Determining the Required Ratio

We need to find the ratio of the number of girls enrolled in Arts to the number of boys enrolled in Science.

Ratio = (Number of girls in Arts) : (Number of boys in Science)

Ratio = 570 : 605

To simplify the ratio, we look for the greatest common divisor (GCD). Both 570 and 605 are divisible by 5.

\( 570 \div 5 = 114 \)

\( 605 \div 5 = 121 \)

So, the simplified ratio is 114 : 121.

Ratio Calculation Summary

• Number of girls in Arts = 570
• Number of boys in Science = 605
• Ratio (Girls in Arts : Boys in Science) = 570 : 605
• Simplified Ratio = 114 : 121

Revision Table: Key Calculations Summary

Additional Information on Percentage and Ratio Calculations

Understanding percentages and ratios is fundamental in data interpretation. A percentage represents a part of a whole, expressed as a fraction of 100. For example, 38% of 1500 means \( \frac{38}{100} \times 1500 \).

A ratio is a comparison of two quantities by division. It can be written as a:b or \(\frac{a}{b}\). Ratios should typically be simplified to their lowest terms by dividing both parts by their greatest common divisor. In this case, we simplified the ratio 570:605 by dividing both numbers by 5 to get 114:121. To ensure it's the lowest term, you might check for common factors of 114 and 121. 114 is \(2 \times 3 \times 19\) and 121 is \(11 \times 11\). They share no common prime factors, so 114:121 is in its simplest form.

When working with enrollment data like this, it's important to pay attention to what base the percentage is calculated from. Here, stream enrollment percentages are based on the total student body (3500), while stream girls percentages are based on the total number of girls (1500). This distinction is crucial for accurate calculations of specific groups within streams.