The table given below shows the distribution percentage of number of…
2023
The table given below shows the distribution percentage of number of candidates qualifying a Common Entrance Test (CET) in six cities A-F during the year 2020 and 2021, along with the ratio of males (M) to females (F) among the qualified candidates. The total number of qualified candidates in all the six cities together during 2020 and 2021 are 3800 and 4600 respectively. Based on the data in the table, answer the question that follows:
City-wise Distribution of CET Qualified Candidates.
Years | 2020 | 2021 | ||
|---|---|---|---|---|
City | Distribution % of Qualified Candidates | Ratio M:F | Distribution % of Qualified Candidates | Ratio M:F |
A | 13% | 8:5 | 24% | 5:7 |
B | 27% | 11:8 | 15% | 12:11 |
C | 11% | 7:4 | 23% | 15:8 |
D | 20% | 2:3 | 17% | 8:9 |
E | 8% | 5:3 | 8% | 1:3 |
F | 21% | 13:8 | 13% | 5:8 |
The average of the number of females qualified from all the six cities together in 2021 is
Answer: C. 400 — ConceptTo find the female count from a group total, split the ratio M:F into m+f equal parts. If the group total is N, the female count is N × f/(m+f). When a…
- A.
320
- B.
360
- C.
400
- D.
440
Show answer & explanation
Correct answer: C
Concept
To find the female count from a group total, split the ratio M:F into m+f equal parts. If the group total is N, the female count is N × f/(m+f).
When a city has p% of an overall total T, its city total is T × p/100. After finding each city’s female count, add the six counts and divide by 6 to obtain their average.
Application
City A: 4600 × 24/100 = 1104 qualified candidates; females = 1104 × 7/(5+7) = 644.
City B: 4600 × 15/100 = 690; females = 690 × 11/(12+11) = 330.
City C: 4600 × 23/100 = 1058; females = 1058 × 8/(15+8) = 368.
City D: 4600 × 17/100 = 782; females = 782 × 9/(8+9) = 414.
City E: 4600 × 8/100 = 368; females = 368 × 3/(1+3) = 276.
City F: 4600 × 13/100 = 598; females = 598 × 8/(5+8) = 368.
Total females = 644 + 330 + 368 + 414 + 276 + 368 = 2400. Therefore, the average = 2400/6 = 400.
Cross-check
The 2021 distribution percentages add to 24+15+23+17+8+13 = 100, so all 4600 candidates are included exactly once. The six female counts sum to 2400, and 400 × 6 = 2400, confirming the average.