Understanding College Vacant Seats Calculation

The question asks us to determine the percentage of vacant seats based on the provided table showing college capacities and student admissions across different streams.

First, let's look at the data presented in the table. It shows four colleges and the number of students admitted to Science, Art, Engineering, and Medical streams, along with the total capacity for each college.

Step-by-Step Calculation of Vacant Seat Percentage

To find the percentage of vacant seats, we need to follow these steps:

1. Calculate the total number of seats available across all colleges.
2. Calculate the total number of students admitted across all streams and colleges.
3. Calculate the total number of vacant seats by subtracting the total admitted students from the total seats.
4. Calculate the percentage of vacant seats relative to the total number of seats.

1. Calculate Total Seats

The total seat capacity is given in brackets next to each college name. Summing them up:

\(\text{Total Seats} = \text{Capacity of Collegew} + \text{Capacity of Collegex} + \text{Capacity of Collegey} + \text{Capacity of Collegez}\)

\(\text{Total Seats} = 500 + 500 + 1000 + 1000\)

\(\text{Total Seats} = 3000\)

There are a total of 3000 seats available across the four colleges.

2. Calculate Total Admitted Students

The number of admitted students is the sum of students in all streams for all colleges. Let's calculate the admitted students for each college first:

• Collegew Admitted: \(100 (\text{Science}) + 100 (\text{Art}) + 50 (\text{Engineering}) + 150 (\text{Medical}) = 400\)
• Collegex Admitted: \(150 (\text{Science}) + 100 (\text{Art}) + 50 (\text{Engineering}) + 50 (\text{Medical}) = 350\)
• Collegey Admitted: \(350 (\text{Science}) + 300 (\text{Art}) + 150 (\text{Engineering}) + 50 (\text{Medical}) = 850\)
• Collegez Admitted: \(300 (\text{Science}) + 350 (\text{Art}) + 150 (\text{Engineering}) + 100 (\text{Medical}) = 900\)

Now, sum the admitted students from all colleges:

\(\text{Total Admitted Students} = 400 + 350 + 850 + 900\)

\(\text{Total Admitted Students} = 2500\)

A total of 2500 students were admitted.

3. Calculate Total Vacant Seats

Vacant seats are the seats that were not filled. We calculate this by subtracting the total admitted students from the total seats:

\(\text{Total Vacant Seats} = \text{Total Seats} - \text{Total Admitted Students}\)

\(\text{Total Vacant Seats} = 3000 - 2500\)

\(\text{Total Vacant Seats} = 500\)

There are 500 vacant seats.

4. Calculate Percentage of Vacant Seats

The percentage of vacant seats is calculated using the formula:

\(\text{Percentage of Vacant Seats} = \left( \frac{\text{Total Vacant Seats}}{\text{Total Seats}} \right) \times 100\)

Substitute the calculated values:

\(\text{Percentage of Vacant Seats} = \left( \frac{500}{3000} \right) \times 100\)

\(\text{Percentage of Vacant Seats} = \left( \frac{1}{6} \right) \times 100\)

\(\text{Percentage of Vacant Seats} \approx 0.16666... \times 100\)

\(\text{Percentage of Vacant Seats} \approx 16.67\)

The percentage of vacant seats is approximately 16.67%.

Based on our calculation, the percentage of vacant seats is 16.67%.

Revision Table: College Seats and Admissions Data

Total Vacant Seats = 500, Total Seats = 3000.

Percentage Vacant = \(\left( \frac{500}{3000} \right) \times 100 \approx 16.67\%\)

Additional Information: Data Interpretation and Percentages

Data interpretation questions often require extracting relevant information from tables or charts and performing calculations like percentages, ratios, or averages. Understanding how to calculate percentages is crucial for these types of problems.

• Percentage: A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
• Calculating Percentage: To find what percentage one quantity (Part) is of another quantity (Whole), the formula is: \(\left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\). In this problem, the 'Part' is the total vacant seats, and the 'Whole' is the total seats available.
• Importance: Calculating percentages helps in comparing different values or understanding proportions within a dataset, such as the proportion of vacant seats relative to total capacity.