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% | 15:5 |
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% |
What is the ratio of the number of female candidates who qualified from states A and C together in 2021 to number of male candidates who qualified from the same two states in the year 2022?
Answer: C. 8307:21944 — ConceptTo find a subgroup count from percentage data, multiply the overall total by the qualification rate, then by the state distribution share, and finally…
- A.
8307:21844
- B.
8407:21944
- C.
8307:21944
- D.
8307:20894
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
To find a subgroup count from percentage data, multiply the overall total by the qualification rate, then by the state distribution share, and finally by the required gender share. For a male-to-female ratio m:f, the male share is m/(m+f) and the female share is f/(m+f).
Application
The total number of qualified candidates in 2021 is 142000 × 45% = 63900.
For state A in 2021, the qualified female count is 63900 × 18% × 4/9 = 5112.
For state C in 2021, the qualified female count is 63900 × 12% × 5/12 = 3195.
Therefore, the 2021 female total for states A and C is 5112 + 3195 = 8307.
The total number of qualified candidates in 2022 is 180000 × 52% = 93600.
For state A in 2022, the qualified male count is 93600 × 20% × 28/45 = 11648.
For state C in 2022, the qualified male count is 93600 × 16% × 11/16 = 10296.
Therefore, the 2022 male total for states A and C is 11648 + 10296 = 21944.
Cross-check
The state distribution percentages add to 100% in each year. The intermediate state totals—11502 and 7668 in 2021, and 18720 and 14976 in 2022—also reconcile with their respective male-to-female splits. Hence the requested ratio is 8307:21944, equivalently 639:1688 after division by 13.