Here are 10 questions related to Inverse Proportion with solutions, tailored for Coal India Legal or general applications in coal and mining industries:

Here are 10 questions related to Inverse Proportion with solutions, tailored for Coal India Legal or general applications in coal and mining industries:

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1. Workers & Time

Q: A group of 12 workers can complete a legal document review in 15 days. How many days will it take if 20 workers are assigned to the same task, assuming work efficiency remains the same?

Solution:

Since the number of workers and the time required are inversely proportional, we use:

W_1 \times T_1 = W_2 \times T_2

12 \times 15 = 20 \times T_2 ]

T_2 = \frac{12 \times 15}{20} = 9 \text{ days}

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2. Trucks & Coal Transport

Q: If 8 trucks take 6 hours to transport coal from a mine, how long will 12 trucks take for the same job?

Solution:

8 \times 6 = 12 \times T_2

T_2 = \frac{8 \times 6}{12} = 4 \text{ hours} ] So, 12 trucks will take 4 hours.

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3. Miners & Extraction Rate

Q: A team of 30 miners extracts a certain amount of coal in 20 days. How many days will it take if 50 miners work at the same rate?

Solution:

30 \times 20 = 50 \times T_2

T_2 = \frac{30 \times 20}{50} = 12 \text{ days} ] So, 50 miners will take 12 days.

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4. Lawyers & Case Handling

Q: A legal team of 5 lawyers takes 40 days to review contracts. If 10 lawyers work, how many days will it take?

Solution:

5 \times 40 = 10 \times T_2

T_2 = \frac{5 \times 40}{10} = 20 \text{ days} ] So, 10 lawyers will take 20 days.

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5. Pumps & Water Drainage

Q: 3 pumps can drain a flooded coal mine in 18 hours. How long will it take if 6 pumps work at the same rate?

Solution:

3 \times 18 = 6 \times T_2

T_2 = \frac{3 \times 18}{6} = 9 \text{ hours} ] So, 6 pumps will take 9 hours.

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6. Machines & Coal Processing

Q: A processing plant with 4 machines completes coal processing in 10 hours. How long will 8 machines take?

Solution:

4 \times 10 = 8 \times T_2

T_2 = \frac{4 \times 10}{8} = 5 \text{ hours} ] So, 8 machines will take 5 hours.

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7. Typists & Legal Documents

Q: 6 typists take 24 hours to type a set of legal documents. How long will 8 typists take?

Solution:

6 \times 24 = 8 \times T_2

T_2 = \frac{6 \times 24}{8} = 18 \text{ hours} ] So, 8 typists will take 18 hours.

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8. Drilling & Borewell Completion

Q: A drilling team of 10 workers completes a borewell in 5 days. How long will a team of 25 workers take?

Solution:

10 \times 5 = 25 \times T_2

T_2 = \frac{10 \times 5}{25} = 2 \text{ days} ] So, 25 workers will take 2 days.

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9. Loaders & Coal Loading

Q: A team of 15 loaders takes 30 hours to load a shipment. How long will a team of 25 loaders take?

Solution:

15 \times 30 = 25 \times T_2

T_2 = \frac{15 \times 30}{25} = 18 \text{ hours} ] So, 25 loaders will take 18 hours.

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10. Guards & Security Monitoring

Q: 20 security guards can monitor a coal site in 12 hours. How long will 30 guards take?

Solution:

20 \times 12 = 30 \times T_2

T_2 = \frac{20 \times 12}{30} = 8 \text{ hours} ] So, 30 guards will take 8 hours.

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These questions are practical applications of inverse proportion in coal mining, logistics, legal teams, and industrial operations. Let me know if you need more!