Calculating the Ratio of Qualified Candidates

This problem requires us to analyze data presented in two tables to find the ratio of female candidates from specific states in one year to male candidates from the same states in another year. We need to use the total number of appeared candidates, the percentage who qualified, the state-wise distribution of qualified candidates, and the male to female ratio within each state.

Step 1: Calculate the Total Number of Qualified Candidates in Each Year

Table 2 provides the total number of candidates who appeared and the overall percentage who qualified from all six states (A-F) for both 2021 and 2022.

• Total Qualified in 2021:
• Total Appeared in 2021 = 142000
• Percentage Qualified in 2021 = 45%
• Total Qualified in 2021 = $\frac{45}{100} \times 142000 = 0.45 \times 142000 = 63900$

• Total Qualified in 2022:
• Total Appeared in 2022 = 180000
• Percentage Qualified in 2022 = 52%
• Total Qualified in 2022 = $\frac{52}{100} \times 180000 = 0.52 \times 180000 = 93600$

Step 2: Calculate Female Candidates Qualified from States A and C in 2021

We need to find the number of female candidates qualified from State A and State C in 2021. Table 1 gives the percentage distribution of qualified candidates by state and the male-female ratio for each state.

• For State A in 2021:
• Percentage of total qualified from State A = 18%
• Number qualified from State A in 2021 = 18% of 63900 = $\frac{18}{100} \times 63900 = 0.18 \times 63900 = 11502$
• Male : Female ratio in State A = 5 : 4
• Total ratio parts = 5 + 4 = 9
• Fraction of females in State A = $\frac{4}{9}$
• Number of female candidates from State A in 2021 = $\frac{4}{9} \times 11502 = 4 \times \frac{11502}{9} = 4 \times 1278 = 5112$

• For State C in 2021:
• Percentage of total qualified from State C = 12%
• Number qualified from State C in 2021 = 12% of 63900 = $\frac{12}{100} \times 63900 = 0.12 \times 63900 = 7668$
• Male : Female ratio in State C = 7 : 5
• Total ratio parts = 7 + 5 = 12
• Fraction of females in State C = $\frac{5}{12}$
• Number of female candidates from State C in 2021 = $\frac{5}{12} \times 7668 = 5 \times \frac{7668}{12} = 5 \times 639 = 3195$

Total female candidates qualified from States A and C in 2021 = (Female from A) + (Female from C)

Total female from A and C in 2021 = $5112 + 3195 = 8307$

Step 3: Calculate Male Candidates Qualified from States A and C in 2022

Now, we find the number of male candidates qualified from State A and State C in 2022.

• For State A in 2022:
• Percentage of total qualified from State A = 20%
• Number qualified from State A in 2022 = 20% of 93600 = $\frac{20}{100} \times 93600 = 0.20 \times 93600 = 18720$
• Male : Female ratio in State A = 28 : 17
• Total ratio parts = 28 + 17 = 45
• Fraction of males in State A = $\frac{28}{45}$
• Number of male candidates from State A in 2022 = $\frac{28}{45} \times 18720 = 28 \times \frac{18720}{45} = 28 \times 416 = 11648$

• For State C in 2022:
• Percentage of total qualified from State C = 16%
• Number qualified from State C in 2022 = 16% of 93600 = $\frac{16}{100} \times 93600 = 0.16 \times 93600 = 14976$
• Male : Female ratio in State C = 11 : 5
• Total ratio parts = 11 + 5 = 16
• Fraction of males in State C = $\frac{11}{16}$
• Number of male candidates from State C in 2022 = $\frac{11}{16} \times 14976 = 11 \times \frac{14976}{16} = 11 \times 936 = 10296$

Total male candidates qualified from States A and C in 2022 = (Male from A) + (Male from C)

Total male from A and C in 2022 = $11648 + 10296 = 21944$

Step 4: Determine the Required Ratio

The question asks for the ratio of the number of female candidates who qualified from states A and C together in 2021 to the number of male candidates who qualified from the same two states in the year 2022.

Required Ratio = (Total female from A and C in 2021) : (Total male from A and C in 2022)

Required Ratio = $8307 : 21944$

Data Tables Used

Conclusion on Qualified Candidate Ratio

Based on the calculations, the ratio of female candidates who qualified from states A and C together in 2021 to the number of male candidates who qualified from the same two states in the year 2022 is 8307 : 21944.

Revision Table: Key Calculations

Additional Information on Data Interpretation

Data interpretation questions in competitive exams often involve understanding percentages, ratios, and how to extract specific information from tables or charts. Key skills include:

• Reading and understanding the labels and units in tables.
• Calculating percentages of given totals.
• Splitting a quantity based on a given ratio.
• Combining data from different parts of the tables to answer a specific question.
• Being careful with calculations, especially multiplication and division involving percentages and ratios.

In this problem, we combined the overall qualification data from Table 2 with the state-specific distribution and gender ratio data from Table 1. This is a common pattern in data interpretation sets.