Analyzing Civil Services Exam Data

The question asks for the percentage rise in the number of candidates who passed the Civil Services Examination from City K between the years 2017 and 2018. We need to extract the relevant data from the provided table and then perform the percentage change calculation.

Extracting Passed Candidates Data for City K

We look at the row for year 2017 and the column for City K (P). The number of candidates who passed from City K in 2017 is 360.

Next, we look at the row for year 2018 and the column for City K (P). The number of candidates who passed from City K in 2018 is 504.

• Number of candidates passed from City K in 2017 = 360
• Number of candidates passed from City K in 2018 = 504

Calculating the Rise in Passed Candidates

The rise in the number of candidates who passed from City K from 2017 to 2018 is the difference between the 2018 value and the 2017 value.

Rise = (Number passed in 2018) - (Number passed in 2017)

Rise = 504 - 360 = 144

Calculating the Percentage Rise

The percentage rise is calculated using the formula:

\( \text{Percentage Rise} = \left( \frac{\text{Rise}}{\text{Original Value}} \right) \times 100 \)

Here, the original value is the number of candidates who passed in the initial year, which is 2017. So, the original value is 360.

\( \text{Percentage Rise} = \left( \frac{144}{360} \right) \times 100 \)

We can simplify the fraction \( \frac{144}{360} \):

\( \frac{144}{360} = \frac{72}{180} = \frac{36}{90} = \frac{18}{45} \)

Both 18 and 45 are divisible by 9:

\( \frac{18}{45} = \frac{18 \div 9}{45 \div 9} = \frac{2}{5} \)

Now, substitute this back into the percentage rise formula:

\( \text{Percentage Rise} = \left( \frac{2}{5} \right) \times 100 \)

\( \text{Percentage Rise} = 0.4 \times 100 \)

\( \text{Percentage Rise} = 40 \)

So, the percentage rise in the number of candidates who passed from City K from year 2017 to year 2018 is 40%.

Revision Table: Data Interpretation Practice

This table summarizes the key figures used in the calculation.

Additional Information: Understanding Percentage Change

Percentage change is a useful concept in data analysis to show how much a value has changed relative to its initial value. It can be a percentage increase (rise) or decrease (fall).

The general formula for percentage change is:

\( \text{Percentage Change} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100 \)

If the result is positive, it's a percentage rise. If the result is negative, it's a percentage fall.

In our case, the Initial Value was the number passed in 2017 (360), and the Final Value was the number passed in 2018 (504).

\( \text{Percentage Change} = \left( \frac{504 - 360}{360} \right) \times 100 \)

\( \text{Percentage Change} = \left( \frac{144}{360} \right) \times 100 \)

\( \text{Percentage Change} = \frac{2}{5} \times 100 = 40 \)

The result is +40, indicating a 40% rise.

This type of calculation is common in quantitative aptitude sections of exams, often presented with tables or graphs.