Table-1 below shows the percentage (%) distribution of candidates who…
2023
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.
State | 2021 Qualified (%) | 2021 Male : Female | 2022 Qualified (%) | 2022 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 states 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?
Answer: A. 5990 — ConceptWhen a table gives the distribution of all qualified candidates, first find the overall qualified total and then allocate that total by each state’s…
- A.
5990
- B.
5900
- C.
5920
- D.
5940
Show answer & explanation
Correct answer: A
Concept
When a table gives the distribution of all qualified candidates, first find the overall qualified total and then allocate that total by each state’s percentage.
For a male:female ratio m:f, the female share is f/(m + f). An average across six states equals the sum of the six eligible female counts divided by 6.
Application
Overall qualified candidates in 2022 = 180,000 × 52/100 = 93,600.
State A: 93,600 × 20/100 × 17/45 = 7,072 qualified females; after excluding four ineligible candidates, 7,072 − 4 = 7,068.
State B: 93,600 × 12/100 × 3/8 = 4,212 qualified females.
State C: 93,600 × 16/100 × 5/16 = 4,680 qualified females.
State D: 93,600 × 15/100 × 11/26 = 5,940 qualified females.
State E: 93,600 × 22/100 × 9/24 = 7,722 qualified females.
State F: 93,600 × 15/100 × 9/20 = 6,318 qualified females.
Eligible female total = 7,068 + 4,212 + 4,680 + 5,940 + 7,722 + 6,318 = 35,940; average = 35,940/6 = 5,990.
Cross-check
Before the eligibility adjustment, the six female counts total 35,944.
Removing the four ineligible candidates gives 35,940; multiplying 5,990 by 6 also gives 35,940.
Therefore, the required average is 5,990.