The question asks us to analyze the provided table showing the number of students enrolled in a Vocational Course (VC) across five different institutes (A, B, C, D, and E) over six years (2014 to 2019). We need to calculate the difference, denoted as 'x', between two specific totals from this table and determine which range this difference falls into.

We are asked to find the difference 'x' between:

1. The total number of students enrolled in VC in Institutes C, D, and E in the year 2017.
2. The total number of students enrolled in Institute B in the years 2015, 2017, and 2019.

Calculating Total Vocational Course Enrollments

First, let's find the total number of students enrolled in Institutes C, D, and E in the year 2017. Looking at the table, the enrollments for 2017 are:

• Institute C (2017): 145 students
• Institute D (2017): 152 students
• Institute E (2017): 178 students

The total enrollment for C, D, and E in 2017 is the sum of these numbers:

\( \text{Total (C, D, E in 2017)} = 145 + 152 + 178 \)

Let's perform the addition:

\( 145 + 152 = 297 \)

\( 297 + 178 = 475 \)

So, the total number of students enrolled in Institutes C, D, and E in 2017 is 475.

Next, let's find the total number of students enrolled in Institute B in the years 2015, 2017, and 2019. Looking at the table, the enrollments for Institute B in these years are:

• Institute B (2015): 127 students
• Institute B (2017): 136 students
• Institute B (2019): 144 students

The total enrollment for Institute B in 2015, 2017, and 2019 is the sum of these numbers:

\( \text{Total (B in 2015, 2017, 2019)} = 127 + 136 + 144 \)

Let's perform the addition:

\( 127 + 136 = 263 \)

\( 263 + 144 = 407 \)

So, the total number of students enrolled in Institute B in 2015, 2017, and 2019 is 407.

Calculating the Difference 'x'

The question states that the total enrollment in C, D, and E in 2017 exceeds the total enrollment in B in 2015, 2017, and 2019 by 'x'. This means 'x' is the difference between the first total and the second total:

\( x = \text{Total (C, D, E in 2017)} - \text{Total (B in 2015, 2017, 2019)} \)

\( x = 475 - 407 \)

Let's perform the subtraction:

\( 475 - 407 = 68 \)

So, the value of 'x' is 68.

Determining the Range for 'x'

Now we need to find which of the given options the value of x (which is 68) lies between:

• Option 1: 60 and 70 (Is 68 between 60 and 70? Yes, \(60 < 68 < 70\)).
• Option 2: 70 and 80 (Is 68 between 70 and 80? No).
• Option 3: 40 and 50 (Is 68 between 40 and 50? No).
• Option 4: 50 and 60 (Is 68 between 50 and 60? No).

The calculated value of x = 68 lies between 60 and 70.

Therefore, the correct range for x is 60 and 70.

Revision Table: Vocational Course Enrollment Analysis

Additional Information on Table Data Interpretation

Interpreting data from tables is a common skill tested in various exams. It involves carefully reading the table structure, understanding the row and column headers, and extracting the specific data points required for calculations. Key aspects include:

• Reading the Axes: Identify what the rows (usually categories like Institutes or years) and columns (usually values or different categories) represent.
• Locating Data Points: Find the intersection of the relevant row and column to get a specific data value. For example, finding the enrollment in Institute D in 2018 requires looking at the row for 'D' and the column for '2018'.
• Performing Calculations: Once data is extracted, perform the requested mathematical operations (addition, subtraction, multiplication, division, percentage calculations, averages, etc.).
• Understanding the Question: Pay close attention to exactly what the question is asking for – whether it's a total, a difference, a ratio, a percentage change, etc.
• Units: While not explicitly stated as units here, understand what the numbers represent (e.g., number of students).

Practice with different types of tables and questions helps improve speed and accuracy in data interpretation.