Read the given passage and answer the questions that follow The following table has the number of enrolled students for a particular course and year. Total number of seats are given in brackets with respect to each course. Number of Enrolled Students BTech MTech MPhilYear
(120)
(30)
(20)MBA
(60)2016 96 24 12 52 2017 110 26 14 57 2018 108 25 13 54 2019 112 28 15 56 2020 104 27 16 48
Which year has the minimum vacant seats?
2019
Understanding Vacant Seats in Course Enrollments
The question asks us to identify the year with the minimum number of vacant seats based on the provided table showing enrolled students and total seats for different courses over several years. To find the year with the minimum vacant seats, we first need to calculate the total vacant seats for each year.
The number of vacant seats for a specific course in a given year is calculated by subtracting the number of enrolled students from the total number of seats available for that course.
$\text{Vacant Seats} = \text{Total Seats} - \text{Enrolled Students}$
The total number of seats for each course is given in brackets next to the course name in the table header:
- BTech: 120 seats
- MTech: 30 seats
- MPhil: 20 seats
- MBA: 60 seats
Now, let's calculate the vacant seats for each course in each year and then find the total vacant seats for that year.
Calculating Vacant Seats per Year
Year 2016:
- BTech Vacant Seats = $120 - 96 = 24$
- MTech Vacant Seats = $30 - 24 = 6$
- MPhil Vacant Seats = $20 - 12 = 8$
- MBA Vacant Seats = $60 - 52 = 8$
- Total Vacant Seats (2016) = $24 + 6 + 8 + 8 = 46$
Year 2017:
- BTech Vacant Seats = $120 - 110 = 10$
- MTech Vacant Seats = $30 - 26 = 4$
- MPhil Vacant Seats = $20 - 14 = 6$
- MBA Vacant Seats = $60 - 57 = 3$
- Total Vacant Seats (2017) = $10 + 4 + 6 + 3 = 23$
Year 2018:
- BTech Vacant Seats = $120 - 108 = 12$
- MTech Vacant Seats = $30 - 25 = 5$
- MPhil Vacant Seats = $20 - 13 = 7$
- MBA Vacant Seats = $60 - 54 = 6$
- Total Vacant Seats (2018) = $12 + 5 + 7 + 6 = 30$
Year 2019:
- BTech Vacant Seats = $120 - 112 = 8$
- MTech Vacant Seats = $30 - 28 = 2$
- MPhil Vacant Seats = $20 - 15 = 5$
- MBA Vacant Seats = $60 - 56 = 4$
- Total Vacant Seats (2019) = $8 + 2 + 5 + 4 = 19$
Year 2020:
- BTech Vacant Seats = $120 - 104 = 16$
- MTech Vacant Seats = $30 - 27 = 3$
- MPhil Vacant Seats = $20 - 16 = 4$
- MBA Vacant Seats = $60 - 48 = 12$
- Total Vacant Seats (2020) = $16 + 3 + 4 + 12 = 35$
Summary of Total Vacant Seats per Year
Let's put the total vacant seats for each year into a table for easy comparison.
| Year | Total Vacant Seats |
|---|---|
| 2016 | 46 |
| 2017 | 23 |
| 2018 | 30 |
| 2019 | 19 |
| 2020 | 35 |
Comparing the total vacant seats for each year:
- 2016: 46 vacant seats
- 2017: 23 vacant seats
- 2018: 30 vacant seats
- 2019: 19 vacant seats
- 2020: 35 vacant seats
The minimum number of vacant seats is 19, which occurred in the year 2019.
Conclusion
By calculating the vacant seats for each course and summing them up for each year, we found that the year 2019 had the lowest total number of vacant seats among the given years.
Revision Table: Course Enrollment Analysis
This section summarizes the key calculation steps involved in finding the minimum vacant seats year.
| Step | Description | Relevant Data Used |
|---|---|---|
| 1 | Identify Total Seats for each course | BTech (120), MTech (30), MPhil (20), MBA (60) |
| 2 | Calculate Vacant Seats for each course in each year | Total Seats, Enrolled Students from the table |
| 3 | Sum course-wise vacant seats to get Total Vacant Seats per year | Vacant Seats calculated in Step 2 |
| 4 | Compare Total Vacant Seats across all years | Total Vacant Seats for 2016, 2017, 2018, 2019, 2020 |
| 5 | Identify the year with the minimum Total Vacant Seats | Result of comparison in Step 4 |
Additional Information: Data Interpretation and Analysis
Analyzing tables with data like course enrollments and seats requires careful interpretation. Key terms like 'enrolled students', 'total seats', and 'vacant seats' are crucial.
- Enrolled Students: The actual number of students registered for a course in a specific year. This data is directly given in the table.
- Total Seats: The maximum capacity or the limit of students that can be admitted into a particular course. This is given as a fixed number for each course across the years.
- Vacant Seats: The number of seats that were not filled in a course during a specific year. This is a derived metric calculated as the difference between total seats and enrolled students. A lower number of vacant seats generally indicates higher demand or more efficient filling of available spots for that year across all courses combined.
When analyzing such data, one might also look at other aspects like enrollment trends over years, popularity of specific courses, or the percentage of seats filled (enrollment rate = (Enrolled Students / Total Seats) * 100). For this particular question, focusing on calculating and comparing total vacant seats was the direct path to the answer.
Important Questions from Data Interpretation
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What is the ratio of total earnings of P to the total earnings of Q?Earnings Days P Q Monday 105 150 Tuesday 96 110 Wednesday 65 122 Thursday 115 106 Friday 130 68 The table below shows the number of toys of 6 different colours sold from a shop during a given period. The table also shows the percentage of toys of each colour which are cars.
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Study the given graph carefully and answer the question that follows. The graph shows the demand and production of different companies.
The ratio between the companies having more production than demand and more demand than production is:
Study the given table and answer the question that follows. The given table shows the number of new employees added to different categories of employees in a company for four years and the number of employees from these categories who left the company every year.
During the period between 2001 and 2004, the total number of Technicians who left the Company is what percentage (rounded off to the nearest integer) of the total number of Technicians who joined the Company?
The given pie-chart shows the percentage distribution of 20,000 employees in a company. Study the given chart and answer the question that follows. If 30% of the employees in department D are females, then how many male employees are there in that department?
