Understanding Vocational Course Enrollment Data

The question asks us to analyze the provided table which shows the number of students enrolled in Vocational Courses (VC) across six different institutes (A, B, C, D, E, & F) over five years (2014 to 2018).

We need to perform two main calculations based on this student enrollment data and then find the percentage relationship between them.

Analyzing Student Enrollment Data from the Table

First, let's look at the data provided in the table:

Calculating Total Enrollment in 2014 for D and F

We need to find the total number of students enrolled for VC in institutes D and F in the year 2014.

• Enrollment in Institute D in 2014: 125
• Enrollment in Institute F in 2014: 165

Total enrollment in D and F in 2014 = Enrollment in D (2014) + Enrollment in F (2014)

Total enrollment in D and F in 2014 = $$125 + 165 = 290$$

Calculating Total Enrollment in 2018 for A, B, and C

Next, we need to find the total number of students enrolled in institutes A, B, and C in the year 2018.

• Enrollment in Institute A in 2018: 205
• Enrollment in Institute B in 2018: 220
• Enrollment in Institute C in 2018: 225

Total enrollment in A, B, and C in 2018 = Enrollment in A (2018) + Enrollment in B (2018) + Enrollment in C (2018)

Total enrollment in A, B, and C in 2018 = $$205 + 220 + 225 = 650$$

Calculating Percentage

The question asks for the total number of students enrolled for VC in institutes D and F in 2014 as a percentage of the total number of students enrolled in institutes A, B, and C in 2018.

Percentage = $$\left( \frac{\text{Total enrollment in D and F in 2014}}{\text{Total enrollment in A, B, C in 2018}} \right) \times 100$$

Percentage = $$\left( \frac{290}{650} \right) \times 100$$

Percentage = $$\left( \frac{29}{65} \right) \times 100$$

Now, let's calculate the value:

$$\frac{29}{65} \approx 0.4461538$$

Percentage $\approx 0.4461538 \times 100 \approx 44.61538$$

Rounding to One Decimal Point

We are asked to round the result to one decimal point. The second decimal digit is 1, which is less than 5, so we round down.

$$44.61538 \approx 44.6$$

So, the total number of students enrolled for VC in institutes D and F in 2014 is approximately 44.6% of the total number of students enrolled in institutes A, B and C in 2018.

Revision Table: Key Calculations

Additional Information on Data Interpretation

This problem involves basic data interpretation from a table, calculating sums and percentages. These types of questions are common in quantitative aptitude sections of exams.

• When working with tables, carefully identify the correct row (institute) and column (year) for the required data points.
• Pay close attention to keywords like "total number", "what percent of", and "correct to one decimal point". These instructions are crucial for accurate calculation and presentation of the final answer.
• Percentage calculation involves finding the ratio of the part to the whole and multiplying by 100. The 'whole' is usually the value that comes after "percent of".
• Rounding rules are important. If the first digit after the desired number of decimal places is 5 or greater, round up the last desired digit. If it is less than 5, keep the last desired digit as it is.

Understanding how to extract relevant data and perform simple arithmetic operations like addition and percentage calculation is key to solving such data interpretation problems involving vocational courses and student enrollment figures.