Analyzing CET Qualified Candidates Data

The question asks for the ratio of the number of females qualified from City D in the year 2020 to the number of females qualified from City E in the year 2021. To find this ratio, we first need to calculate the number of females qualified from each city in the respective years using the provided data table and total qualified candidates.

Understanding the Given Data

We are given the following information:

• Total qualified candidates in 2020: 3800
• Total qualified candidates in 2021: 4600
• A table showing the distribution percentage of qualified candidates in six cities (A-F) for both years and the ratio of males (M) to females (F) among them.

Step-by-Step Calculation

1. Calculate the number of qualified candidates in City D in 2020.

The distribution percentage for City D in 2020 is 20%.

Total qualified candidates in 2020 = 3800.

Number of qualified candidates in City D (2020) = \( 20\% \text{ of } 3800 \)

\( = \frac{20}{100} \times 3800 \)

\( = 0.20 \times 3800 \)

\( = 760 \)

2. Calculate the number of females qualified from City D in 2020.

The ratio of Males to Females in City D in 2020 is 2 : 3.

Total ratio parts = \( 2 + 3 = 5 \).

The female part of the ratio is 3.

Number of females in City D (2020) = \( \frac{\text{Female Ratio Part}}{\text{Total Ratio Parts}} \times \text{Total qualified candidates in City D (2020)} \)

\( = \frac{3}{5} \times 760 \)

\( = 3 \times \frac{760}{5} \)

\( = 3 \times 152 \)

\( = 456 \)

So, 456 females qualified from City D in 2020.

3. Calculate the number of qualified candidates in City E in 2021.

The distribution percentage for City E in 2021 is 8%.

Total qualified candidates in 2021 = 4600.

Number of qualified candidates in City E (2021) = \( 8\% \text{ of } 4600 \)

\( = \frac{8}{100} \times 4600 \)

\( = 0.08 \times 4600 \)

\( = 368 \)

4. Calculate the number of females qualified from City E in 2021.

The ratio of Males to Females in City E in 2021 is 1 : 3.

Total ratio parts = \( 1 + 3 = 4 \).

The female part of the ratio is 3.

Number of females in City E (2021) = \( \frac{\text{Female Ratio Part}}{\text{Total Ratio Parts}} \times \text{Total qualified candidates in City E (2021)} \)

\( = \frac{3}{4} \times 368 \)

\( = 3 \times \frac{368}{4} \)

\( = 3 \times 92 \)

\( = 276 \)

So, 276 females qualified from City E in 2021.

5. Calculate the ratio of females qualified from City D (2020) to City E (2021).

Ratio = (Females in City D, 2020) : (Females in City E, 2021)

Ratio = \( 456 : 276 \)

To simplify the ratio, find the greatest common divisor (GCD) or divide by common factors.

Both 456 and 276 are divisible by 4:

\( 456 \div 4 = 114 \)

\( 276 \div 4 = 69 \)

The ratio becomes \( 114 : 69 \).

Both 114 and 69 are divisible by 3:

\( 114 \div 3 = 38 \)

\( 69 \div 3 = 23 \)

The simplified ratio is \( 38 : 23 \).

Comparing this ratio with the given options, we find that it matches option 4.

Revision Table: CET Qualified Candidate Analysis

Ratio of females (City D, 2020) to females (City E, 2021) = \( 456 : 276 = 38 : 23 \).

Additional Information: Data Interpretation Concepts

This question involves data interpretation from a table, specifically dealing with percentages and ratios. Key concepts used here include:

• Percentage Distribution: Calculating a part of a total amount based on a given percentage. The formula is \( \text{Part} = \frac{\text{Percentage}}{100} \times \text{Total} \).
• Ratio Division: Dividing a quantity into parts according to a given ratio. If a quantity \(Q\) is divided in the ratio \(a:b\), the two parts are \( \frac{a}{a+b} \times Q \) and \( \frac{b}{a+b} \times Q \). In this problem, the qualified candidates in a city are divided between males and females based on the male:female ratio.
• Ratio Simplification: Reducing a ratio to its simplest form by dividing both parts by their greatest common divisor. This makes ratios easier to compare and understand.

Such data interpretation problems are common in competitive exams and require careful reading of the table and precise calculations.