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In a state sericulture development drive, three agricultural districts—District R, District S, and District T—produced a cumulative total of 3,000 kg3,000\text{ kg} of raw silk, consisting exclusively of Mulberry silk and Eri silk. Across all three districts combined, Mulberry silk accounted for 60%60\% of the total raw silk production. In District R, total raw silk production was 1,000 kg1,000\text{ kg}, of which 65%65\% was Mulberry silk. District S produced a total of 1,200 kg1,200\text{ kg} of raw silk with a Mulberry silk to Eri silk production ratio of 7:57 : 5. The remaining raw silk was produced in District T. What is the absolute difference between the quantity of Mulberry silk and the quantity of Eri silk produced in District T?

  1. 100 kg100\text{ kg}Cevap
  2. B
    150 kg150\text{ kg}
  3. C
    200 kg200\text{ kg}
  4. D
    50 kg50\text{ kg}

Cevap

The absolute difference between Mulberry silk and Eri silk produced in District T is 100 kg100\text{ kg}.
Total raw silk produced is 3,000 kg3,000\text{ kg}, making total Mulberry silk 1,800 kg1,800\text{ kg} (60%60\%) and total Eri silk 1,200 kg1,200\text{ kg}. District R produces 650 kg650\text{ kg} Mulberry and 350 kg350\text{ kg} Eri silk. District S produces 700 kg700\text{ kg} Mulberry and 500 kg500\text{ kg} Eri silk. Consequently, District T produces 450 kg450\text{ kg} Mulberry silk (1,800−1,3501,800 - 1,350) and 350 kg350\text{ kg} Eri silk (1,200−8501,200 - 850). The difference between Mulberry and Eri silk in District T is 450−350=100 kg450 - 350 = 100\text{ kg}.

Adım Adım Çözüm

1
Calculate overall production totals for Mulberry and Eri silk
Total Mulberry silk = 60% of 3,000 kg=1,800 kg60\% \text{ of } 3,000\text{ kg} = 1,800\text{ kg}. Total Eri silk = 3,000 kg−1,800 kg=1,200 kg3,000\text{ kg} - 1,800\text{ kg} = 1,200\text{ kg}.
Establishing aggregate category totals provides the basis to determine missing District T values.
2
Determine breakdown for District R and District S
District R: Total = 1,000 kg1,000\text{ kg}, Mulberry = 65%×1,000=650 kg65\% \times 1,000 = 650\text{ kg}, Eri = 350 kg350\text{ kg}. District S: Total = 1,200 kg1,200\text{ kg}, Mulberry = 712×1,200=700 kg\frac{7}{12} \times 1,200 = 700\text{ kg}, Eri = 512×1,200=500 kg\frac{5}{12} \times 1,200 = 500\text{ kg}.
Extract specific entity values from given percentage and ratio conditions.
3
Derive Mulberry and Eri silk quantities for District T
District T Mulberry = 1,800−(650+700)=450 kg1,800 - (650 + 700) = 450\text{ kg}. District T Eri = 1,200−(350+500)=350 kg1,200 - (350 + 500) = 350\text{ kg}.
Subtracting known district totals from overall state totals yields District T quantities.
4
Calculate the absolute difference for District T
Difference = 450 kg−350 kg=100 kg450\text{ kg} - 350\text{ kg} = 100\text{ kg}.
Directly answers the final prompt query.

Anahtar Kavram

Data extraction, multi-entity category balance, and multi-step quantitative calculation from unstructured paragraph data.
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Konular

Caselets and Paragraph-Based Data

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