Solving the Entrance Exam Qualification Data Problem

This question asks us to find the percentage of the total number of students qualifying an Entrance Exam from schools A-G in 2021 compared to the total number of students qualifying from the same schools in 2020. We are given the percentage distribution of qualified students for each school in both years and the absolute number of students qualifying only from School G for both years.

Understanding the Data Provided

The table shows the distribution of qualified students by percentage for seven schools (A through G) in 2020 and 2021. The key piece of information is the actual number of students from School G in both years: 90 in 2020 and 135 in 2021. Since the percentages for each year add up to 100% for all schools A-G, knowing the absolute number for one school (G) and its percentage allows us to find the total number of qualified students across all schools for that year.

Calculating Total Qualified Students in 2020

In 2020, School G represents 12% of the total qualified students. We know that 90 students qualified from School G in 2020. Let $T_{2020}$ be the total number of students qualifying from schools A-G in 2020.

According to the data:

12% of $T_{2020} = 90$

This can be written as:

$\frac{12}{100} \times T_{2020} = 90$

To find $T_{2020}$, we rearrange the equation:

$T_{2020} = \frac{90 \times 100}{12}$

$T_{2020} = \frac{9000}{12}$

$T_{2020} = 750$

So, the total number of students qualifying from all schools A-G in 2020 was 750.

Calculating Total Qualified Students in 2021

In 2021, School G represents 15% of the total qualified students. We know that 135 students qualified from School G in 2021. Let $T_{2021}$ be the total number of students qualifying from schools A-G in 2021.

According to the data:

15% of $T_{2021} = 135$

This can be written as:

$\frac{15}{100} \times T_{2021} = 135$

To find $T_{2021}$, we rearrange the equation:

$T_{2021} = \frac{135 \times 100}{15}$

$T_{2021} = \frac{13500}{15}$

$T_{2021} = 900$

So, the total number of students qualifying from all schools A-G in 2021 was 900.

Calculating the Percentage of 2021 Total with Reference to 2020 Total

The question asks for the percentage of the number of students qualifying in 2021 with reference to 2020. This means we need to calculate $\left(\frac{T_{2021}}{T_{2020}}\right) \times 100\%$.

We have $T_{2020} = 750$ and $T_{2021} = 900$.

Percentage = $\left(\frac{900}{750}\right) \times 100\%$

Percentage = $\left(\frac{90}{75}\right) \times 100\%$

Percentage = $\left(\frac{6}{5}\right) \times 100\%$

Percentage = $1.2 \times 100\%$

Percentage = 120%

Thus, the percentage of the number of students qualifying from Schools A-G together in 2021 with reference to 2020 is 120%.

Revision Table: Key Calculations

Final Calculation: Percentage change = $\left(\frac{\text{Total 2021}}{\text{Total 2020}}\right) \times 100\% = \left(\frac{900}{750}\right) \times 100\% = 120\%$.

Additional Information: Percentage Calculations Explained

Percentage is a way of expressing a number as a fraction of 100. In data interpretation problems, percentages are frequently used to show distribution, change, or comparison.

• Percentage Distribution: This shows how a total is divided among different categories. In this problem, the total number of qualified students in a year is divided among schools A-G, with each school getting a certain percentage. The sum of these percentages for all categories is 100%.
• Calculating Total from Percentage: If you know the percentage value of a part and the actual value of that part, you can find the total. The formula is: Total = $\left(\frac{\text{Part Value}}{\text{Percentage of Part}}\right) \times 100$. We used this concept to find the total qualified students from the data for School G.
• Percentage Change or Comparison: To express one value (Value A) as a percentage of another value (Value B), the formula is $\left(\frac{\text{Value A}}{\text{Value B}}\right) \times 100\%$. If Value A is greater than Value B, the percentage will be over 100%, indicating growth or a larger quantity relative to the reference. If Value A is less than Value B, the percentage will be less than 100%, indicating a decrease or a smaller quantity. In this question, we compared the 2021 total to the 2020 total.

Understanding these basic percentage concepts is crucial for solving data interpretation questions based on percentages and distributions.