What is the total number of female participants in sports events E1 and E3…
2024
What is the total number of female participants in sports events E1 and E3 together ?
Answer: D. 4334 — Concept: when a group of N members is divided in the ratio M : F, a ratio part is a share and not a count, so the number of females is N × F/(M + F). Counts…
- A.
4274
- B.
4308
- C.
4326
- D.
4334
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept: when a group of N members is divided in the ratio M : F, a ratio part is a share and not a count, so the number of females is N × F/(M + F). Counts of the same category are additive across independent groups, so the female total for two events together is simply the sum of every group's own female share.
Application: read only the E1 and E3 columns of the table and apply N × F/(M + F) to each country's row.
Country | E1: N, M : F → females | E3: N, M : F → females |
|---|---|---|
India | 480, 2 : 1 → 480 × 1/3 = 160 | 700, 5 : 2 → 700 × 2/7 = 200 |
US | 1280, 5 : 3 → 1280 × 3/8 = 480 | 1500, 2 : 1 → 1500 × 1/3 = 500 |
China | 1100, 7 : 4 → 1100 × 4/11 = 400 | 1240, 3 : 1 → 1240 × 1/4 = 310 |
Russia | 1300, 8 : 5 → 1300 × 5/13 = 500 | 1500, 8 : 7 → 1500 × 7/15 = 700 |
England | 800, 3 : 1 → 800 × 1/4 = 200 | 900, 5 : 4 → 900 × 4/9 = 400 |
Germany | 650, 16 : 9 → 650 × 9/25 = 234 | 750, 2 : 1 → 750 × 1/3 = 250 |
Total | 1974 | 2360 |
E1 female total: 160 + 480 + 400 + 500 + 200 + 234 = 1974
E3 female total: 200 + 500 + 310 + 700 + 400 + 250 = 2360
Female participants in E1 and E3 together: 1974 + 2360 = 4334
Cross-check: E1 carries 5610 participants and E3 carries 6590, so the two events together involve 12200 people. The male shares are 5610 − 1974 = 3636 and 6590 − 2360 = 4230, i.e. 7866 males in all, and 7866 + 4334 = 12200, so every participant is accounted for. The E2 columns are never used here, and a ratio part must never be read as a count — India's 2 : 1 in E1 means one-third of 480 are female, not 1 out of 480.
Total number of female participants in E1 and E3 together = 4334.