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Difficulty: MediumCaselets and Paragraph-Based Data

In a state e-governance initiative, a total of 2,4002,400 Common Service Centers (CSCs) are distributed across three districts: District P, District Q, and District R. District P contains 30%30\% of the total CSCs. The ratio of the total number of CSCs in District Q to those in District R is 4:34:3. Each CSC is operated by either a male or a female entrepreneur. In District P, 25%25\% of the CSCs are operated by female entrepreneurs. The number of female-operated CSCs in District Q is 50%50\% more than the number of female-operated CSCs in District P. If the total number of female-operated CSCs across all three districts combined is 600600, what is the ratio of male-operated CSCs in District Q to the female-operated CSCs in District R?

  1. A
    29:1129:11
  2. B
    23:923:9
  3. 23:523:5Answer
  4. D
    5:235:23

Answer

The correct ratio is 23:523:5.
Based on the text, District Q has a total of 960 CSCs and District P has 180 female-operated CSCs. Since District Q has 50% more female-operated CSCs than P, it has 270 female-operated CSCs. This leaves 690 male-operated CSCs in Q. Since the total female-operated CSCs across all districts is 600, District R has 600 - (180 + 270) = 150 female-operated CSCs. The ratio of male-operated CSCs in Q to female-operated CSCs in R is 690:150, which simplifies to 23:5.

Step-by-Step Solution

1
Calculate the total number of CSCs in each district.
District P = 720. District Q = 960. District R = 720.
District P has 30% of 2,400 = 720. The remaining 1,680 CSCs are divided between Q and R in a 4:3 ratio. District Q = (4/7) * 1,680 = 960. District R = (3/7) * 1,680 = 720.
2
Calculate the number of female-operated CSCs in Districts P and Q.
Female in P = 180. Female in Q = 270.
Female CSCs in P = 25% of 720 = 180. Female CSCs in Q is 50% more than in P, meaning 180 + (0.50 * 180) = 180 + 90 = 270.
3
Calculate the number of female-operated CSCs in District R.
Female in R = 150.
Total female CSCs = 600. Female in R = Total - (Female P + Female Q) = 600 - (180 + 270) = 600 - 450 = 150.
4
Calculate the number of male-operated CSCs in District Q.
Male in Q = 690.
Total CSCs in Q (960) - Female in Q (270) = 690.
5
Find the requested ratio.
23:5
Ratio of Male in Q to Female in R = 690 : 150. Dividing both sides by 30 gives 23 : 5.

Key Concept

Data Extraction and Percentage Multi-step Calculations in Caselets
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Topics

Caselets and Paragraph-Based Data

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