Table-1 below shows the percentage (%) distribution of candidates who qualified in a competitive examination from six different states A - F during the two years 2021 and 2022, along with the ratio of Males to females among them and Table-2 shows the total number of candidates who appeared and percentage (%) of candidates who qualified from all the six states A - F in same two years. Based on the data in the tables, answer the questions that follow : Table - 1: State-wise Details of Qualified Candidates in 2021 and 2022. Year/State 2021 2022 Qualified (%) Male ∶ Female Qualified (%) Male ∶ Female A 18% 5 ∶ 4 20% 28 ∶ 17 B 16% 3 ∶ 1 12% 5 ∶ 3 C 12% 7 ∶ 5 16% 11 ∶ 5 D 16% 13 ∶ 11 15% 15 ∶ 11 E 25% 13 ∶ 12 22% 15 ∶ 9 F 13% 8 ∶ 1 15% 11 ∶ 9 Table -2 Year-wise Details of Appeared and Qualified (%) Candidates Year Total Appeared from state A-F Percentage (%) Qualified from States A-F 2021 142000 45% 2022 180000 52%
In 2022 for state A, if four female candidates who qualified are not eligible, then what is the average number of female candidates who qualified (and eligible) from all the six states together in the year 2022?
5990
This problem requires us to analyze data from two tables related to a competitive examination in 2021 and 2022 across six states (A-F). We need to find the average number of eligible female candidates who qualified from all six states in 2022, considering a specific condition for state A.
First, let's understand the data provided in the tables:
| Table - 1: State-wise Details of Qualified Candidates | ||||
|---|---|---|---|---|
| Year/State | 2021 | 2022 | ||
| Qualified (%) | Male & Female Ratio | Qualified (%) | Male & Female Ratio | |
| A | 18% | 5 ∶ 4 | 20% | 28 ∶ 17 |
| B | 16% | 3 ∶ 1 | 12% | 5 ∶ 3 |
| C | 12% | 7 ∶ 5 | 16% | 11 ∶ 5 |
| D | 16% | 13 ∶ 11 | 15% | 15 ∶ 11 |
| E | 25% | 13 ∶ 12 | 22% | 15 ∶ 9 |
| F | 13% | 8 ∶ 1 | 15% | 11 ∶ 9 |
| Table - 2: Year-wise Details of Appeared and Qualified Candidates | ||
|---|---|---|
| Year | Total Appeared from state A-F | Percentage (%) Qualified from States A-F |
| 2021 | 142000 | 45% |
| 2022 | 180000 | 52% |
Analyzing Competitive Examination Data for 2022
The question focuses on the year 2022. We need to find the average number of eligible female candidates who qualified from all six states (A to F).
Calculating Total Qualified Candidates in 2022
From Table-2, we know the total number of candidates who appeared from all states in 2022 and the overall percentage of candidates who qualified in 2022.
- Total Appeared in 2022 = 180000
- Percentage Qualified in 2022 = 52%
The total number of candidates who qualified from all six states in 2022 is:
\[ \text{Total Qualified}_{2022} = \text{Total Appeared}_{2022} \times \frac{\text{Percentage Qualified}_{2022}}{100} \] \[ \text{Total Qualified}_{2022} = 180000 \times \frac{52}{100} \] \[ \text{Total Qualified}_{2022} = 1800 \times 52 = 93600 \]So, a total of 93600 candidates qualified from all six states in 2022.
Determining State-wise Qualified and Female Candidates
Table-1 gives the percentage distribution of these 93600 qualified candidates among the six states (A-F) for 2022 and the Male to Female ratio for qualified candidates within each state.
Let's calculate the number of qualified candidates from each state and then the number of qualified female candidates using the given ratios.
| State | % Qualified from State (2022) | Number of Qualified Candidates (2022) | Male : Female Ratio (2022) | Total Ratio Parts | Fraction of Female | Number of Qualified Female Candidates (2022) |
|---|---|---|---|---|---|---|
| A | 20% | \(20\% \text{ of } 93600 = \frac{20}{100} \times 93600 = 18720\) | 28 : 17 | \(28 + 17 = 45\) | \(\frac{17}{45}\) | \(\frac{17}{45} \times 18720 = 17 \times 416 = 7072\) |
| B | 12% | \(12\% \text{ of } 93600 = \frac{12}{100} \times 93600 = 11232\) | 5 : 3 | \(5 + 3 = 8\) | \(\frac{3}{8}\) | \(\frac{3}{8} \times 11232 = 3 \times 1404 = 4212\) |
| C | 16% | \(16\% \text{ of } 93600 = \frac{16}{100} \times 93600 = 14976\) | 11 : 5 | \(11 + 5 = 16\) | \(\frac{5}{16}\) | \(\frac{5}{16} \times 14976 = 5 \times 936 = 4680\) |
| D | 15% | \(15\% \text{ of } 93600 = \frac{15}{100} \times 93600 = 14040\) | 15 : 11 | \(15 + 11 = 26\) | \(\frac{11}{26}\) | \(\frac{11}{26} \times 14040 = 11 \times 540 = 5940\) |
| E | 22% | \(22\% \text{ of } 93600 = \frac{22}{100} \times 93600 = 20592\) | 15 : 9 | \(15 + 9 = 24\) | \(\frac{9}{24} = \frac{3}{8}\) | \(\frac{3}{8} \times 20592 = 3 \times 2574 = 7722\) |
| F | 15% | \(15\% \text{ of } 93600 = \frac{15}{100} \times 93600 = 14040\) | 11 : 9 | \(11 + 9 = 20\) | \(\frac{9}{20}\) | \(\frac{9}{20} \times 14040 = 9 \times 702 = 6318\) |
Total and Eligible Female Candidates
Now, let's sum the number of qualified female candidates from all six states in 2022:
\[ \text{Total Qualified Females}_{2022} = 7072 + 4212 + 4680 + 5940 + 7722 + 6318 \] \[ \text{Total Qualified Females}_{2022} = 35944 \]The question states that in 2022 for state A, four female candidates who qualified are not eligible. The total number of eligible female candidates from all states is the total qualified female candidates minus the ineligible ones from State A.
\[ \text{Total Eligible Females}_{2022} = \text{Total Qualified Females}_{2022} - \text{Ineligible Females from State A} \] \[ \text{Total Eligible Females}_{2022} = 35944 - 4 = 35940 \]So, there are 35940 eligible female candidates who qualified from all six states in 2022.
Finding Average Eligible Female Candidates Across States
To find the average number of eligible female candidates from all six states, we divide the total number of eligible female candidates by the number of states (which is 6).
\[ \text{Average Eligible Females} = \frac{\text{Total Eligible Females}_{2022}}{\text{Number of States}} \] \[ \text{Average Eligible Females} = \frac{35940}{6} \] \[ \text{Average Eligible Females} = 5990 \]The average number of eligible female candidates who qualified from all the six states together in the year 2022 is 5990.
Competitive Exam Data Analysis Revision
| Calculation Step | Value |
|---|---|
| Total Appeared Candidates (2022) | 180000 |
| Percentage Qualified (2022) | 52% |
| Total Qualified Candidates (2022) | 93600 |
| Total Qualified Female Candidates (2022) | 35944 |
| Ineligible Female Candidates from State A | 4 |
| Total Eligible Female Candidates (2022) | 35940 |
| Number of States | 6 |
| Average Eligible Female Candidates (2022) | 5990 |
Additional Information on Data Interpretation
Data interpretation questions like this one test your ability to extract, process, and calculate information from tables and charts. Key skills include:
- Carefully reading the question to understand exactly what is being asked (e.g., total vs. state-wise, qualified vs. appeared, eligible vs. qualified).
- Understanding percentages and how to calculate actual numbers from percentages of a total.
- Working with ratios to divide a total quantity into parts according to the ratio.
- Paying attention to specific conditions or exceptions mentioned in the question (like the ineligible candidates from State A).
- Performing arithmetic calculations accurately.
Always break down the problem into smaller, manageable steps, as demonstrated in the solution. This helps avoid errors and makes the process clear.
Important Questions from Tabulation
The table shows District-wise data of a number of primary school teachers posted in schools of a city.
Study the table and answer the question:
District
Male teachers
Female teachers
East
1650
2375
North
1075
2651
West
1280
1520
South
1170
1085
Central
690
859
What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?Table shows income (in Rs. ) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38500
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
What is the ratio of salary of Varun to his income other than salary?Study the table and answer the question:
Income (Rs.)
No. of persons
Less than 200
12
Less than 250
26
Less than 300
34
Less than 350
40
Less than 400
50
What is the percentage of persons earning Rs. 250 or more?The following table shows the annual profit of a company (in Rs. lakh).
2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
The period which has the maximum percentage increase in profit over the previous year is:
The table given below shows the number of persons participating in a survey from 6 different states.
States Persons S1 100 S2 200 S3 400 S4 500 S5 600 S6 800 What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?
