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Difficulty: MediumCaselets and Paragraph-Based Data

In a municipal solid waste management drive across three processing centers—Plant North, Plant South, and Plant East—a total of 10,000 tonnes10,000\text{ tonnes} of waste was processed in a month.

- Plant North processed 30%30\% of the total waste. Of the waste processed at Plant North, 60%60\% was biodegradable and the rest was non-biodegradable.
- Plant South processed 1.51.5 times the amount of non-biodegradable waste processed by Plant North. The ratio of biodegradable to non-biodegradable waste processed at Plant South was 4:34 : 3.
- Plant East processed the remaining waste, with a ratio of biodegradable to non-biodegradable waste of 5:25 : 2.

Based on the information provided above, which of the following statements are correct?

  1. The total quantity of biodegradable waste processed across all three plants combined is 6,200 tonnes6,200\text{ tonnes}.Answer
  2. The ratio of non-biodegradable waste processed by Plant South to that processed by Plant East is 9:49 : 4.Answer
  3. C
    Plant East processed 30%30\% of the total waste collected across all three plants.
  4. D
    Plant South processed more non-biodegradable waste than the biodegradable waste processed by Plant North.

Answer

The statements confirming that total biodegradable waste across all plants is 6,200 tonnes and that the ratio of non-biodegradable waste between Plant South and Plant East is 9 : 4 are correct.
The total biodegradable waste is indeed 1,800+2,400+2,000=6,200 tonnes1,800 + 2,400 + 2,000 = 6,200\text{ tonnes}, making the first statement correct. Furthermore, comparing non-biodegradable waste of Plant South (1,800 tonnes1,800\text{ tonnes}) and Plant East (800 tonnes800\text{ tonnes}) gives the ratio 1,800:800=9:41,800 : 800 = 9 : 4, making the second statement correct.

Step-by-Step Solution

1
Calculate waste quantities for Plant North.
Total = 3,000 tonnes3,000\text{ tonnes}; Biodegradable = 1,800 tonnes1,800\text{ tonnes}; Non-biodegradable = 1,200 tonnes1,200\text{ tonnes}.
Plant North processed 30%30\% of 10,000 tonnes=3,000 tonnes10,000\text{ tonnes} = 3,000\text{ tonnes}. Biodegradable is 60%60\% of 3,000=1,800 tonnes3,000 = 1,800\text{ tonnes}, leaving 1,200 tonnes1,200\text{ tonnes} non-biodegradable.
2
Calculate waste quantities for Plant South.
Non-biodegradable = 1,800 tonnes1,800\text{ tonnes}; Biodegradable = 2,400 tonnes2,400\text{ tonnes}; Total = 4,200 tonnes4,200\text{ tonnes}.
Non-biodegradable at South is 1.5×1,200=1,800 tonnes1.5 \times 1,200 = 1,800\text{ tonnes}. Given Bio : Non-bio ratio of 4:34 : 3, 3 parts=1,800 tonnes  ⟹  1 part=600 tonnes3\text{ parts} = 1,800\text{ tonnes} \implies 1\text{ part} = 600\text{ tonnes}. Thus, Biodegradable = 4×600=2,400 tonnes4 \times 600 = 2,400\text{ tonnes}.
3
Calculate waste quantities for Plant East.
Total = 2,800 tonnes2,800\text{ tonnes}; Biodegradable = 2,000 tonnes2,000\text{ tonnes}; Non-biodegradable = 800 tonnes800\text{ tonnes}.
Remaining total waste = 10,000−(3,000+4,200)=2,800 tonnes10,000 - (3,000 + 4,200) = 2,800\text{ tonnes}. Given Bio : Non-bio ratio of 5:25 : 2, total parts = 77. 1 part=400 tonnes1\text{ part} = 400\text{ tonnes}. Biodegradable = 5×400=2,000 tonnes5 \times 400 = 2,000\text{ tonnes} and Non-biodegradable = 2×400=800 tonnes2 \times 400 = 800\text{ tonnes}.
4
Verify each statement against calculated values.
Total Biodegradable = 1,800+2,400+2,000=6,200 tonnes1,800 + 2,400 + 2,000 = 6,200\text{ tonnes} (True). South Non-bio : East Non-bio = 1,800:800=9:41,800 : 800 = 9 : 4 (True). Plant East share = 2,800/10,000=28%2,800 / 10,000 = 28\% (False). South Non-bio (1,8001,800) vs North Bio (1,8001,800) are equal (False).
Comparing calculated numerical values directly evaluates statement validity.

Key Concept

Caselet Data Extraction and Multi-Step Proportionate Allocation
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Topics

Caselets and Paragraph-Based Data

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