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Zorluk: Çok zorCaselets and Paragraph-Based Data

A State Public Service Commission conducted a detailed employment survey across three major districts: District A, District B, and District C. The total workforce across all three districts combined is 100,000100,000.

- District A accounts for 40%40\% of the total workforce, and the ratio of male to female workers in District A is 3:23 : 2.
- District B has a total workforce that is 25%25\% greater than the total workforce of District A. Females constitute 44%44\% of District B's workforce.
- District C comprises the remaining workforce across the three districts, with a male-to-female ratio of 3:23 : 2.
- Across all three districts combined, 25%25\% of the total female workforce is employed in the government sector.
- Specifically, 30%30\% of females in District A and 20%20\% of females in District B are employed in the government sector, while the remaining government-employed females work in District C.

Based on the given information, what is the ratio of the number of female government sector workers in District C to the total number of male workers across all three districts combined?

  1. 13:58013 : 580Cevap
  2. B
    13:23613 : 236
  3. C
    13:6013 : 60
  4. D
    1:401 : 40

Cevap

The ratio of the number of female government sector workers in District C to the total number of male workers across all three districts combined is 13:58013 : 580.
The total female government workers across all districts is 10,500 (25% of 42,000 total females). Subtracting District A's 4,800 and District B's 4,400 yields 1,300 government females in District C. The total male population across all three districts is 58,000 (24,000 + 28,000 + 6,000). The ratio 1,300 : 58,000 simplifies directly to 13 : 580.

Adım Adım Çözüm

1
Calculate total workforce and gender breakdown for District A
Total workforce of District A = 40%40\% of 100,000=40,000100,000 = 40,000. With a Male:Female ratio of 3:23:2, Male workforce = 35×40,000=24,000\frac{3}{5} \times 40,000 = 24,000 and Female workforce = 25×40,000=16,000\frac{2}{5} \times 40,000 = 16,000.
Establishing District A numbers is required as the baseline for District B and total female count.
2
Calculate total workforce and gender breakdown for District B
Workforce of District B = 1.25×40,000=50,0001.25 \times 40,000 = 50,000. Female workforce = 44%44\% of 50,000=22,00050,000 = 22,000. Male workforce = 50,000−22,000=28,00050,000 - 22,000 = 28,000.
District B's population is given relative to District A.
3
Determine workforce and gender breakdown for District C
Workforce of District C = 100,000−(40,000+50,000)=10,000100,000 - (40,000 + 50,000) = 10,000. With Male:Female ratio of 3:23:2, Male workforce = 35×10,000=6,000\frac{3}{5} \times 10,000 = 6,000 and Female workforce = 25×10,000=4,000\frac{2}{5} \times 10,000 = 4,000.
District C contains the residual workforce from the total 100,000100,000.
4
Calculate overall male and female workforce totals
Total Male workforce = 24,000+28,000+6,000=58,00024,000 + 28,000 + 6,000 = 58,000. Total Female workforce = 16,000+22,000+4,000=42,00016,000 + 22,000 + 4,000 = 42,000.
The total male workforce forms the denominator of the required ratio.
5
Calculate government-employed females in District C
Total Female Government Workers = 25%25\% of 42,000=10,50042,000 = 10,500. District A Female Government Workers = 30%30\% of 16,000=4,80016,000 = 4,800. District B Female Government Workers = 20%20\% of 22,000=4,40022,000 = 4,400. District C Female Government Workers = 10,500−(4,800+4,400)=1,30010,500 - (4,800 + 4,400) = 1,300.
Subtracting District A and B government females from the overall total isolates District C's count.
6
Compute the final ratio
Ratio = 1,30058,000=13580\frac{1,300}{58,000} = \frac{13}{580} or 13:58013 : 580.
Simplifying the fraction gives the required final ratio.

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Multi-step quantitative interpretation of paragraph data involving percentage base shifts and system of equations.
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