Which of the following statements shows inverse proportions?

Options

A. Number of workers and time taken to complete the work.
B. Speed of vehicle and distance covered.
C. Use of electricity and electricity bill.
D. None of these

Answer

To determine which of the statements shows inverse proportions, we need to understand the concept of inverse proportion. Inverse proportion means that as one quantity increases, the other quantity decreases in such a way that their product remains constant.

### Step-by-step Solution:

1. **Understand Inverse Proportion**:
- Inverse proportion can be expressed mathematically as \( A \times B = K \), where \( K \) is a constant. This means if \( A \) increases, \( B \) must decrease to keep \( K \) constant.

2. **Analyze the First Statement**:
- **Number of Workers and Time Taken to Complete Work**:
- If the number of workers increases, the time taken to complete the work decreases, and vice versa. This indicates an inverse relationship. Therefore, this statement shows inverse proportion.

3. **Analyze the Second Statement**:
- **Speed of Vehicle and Distance Covered**:
- The relationship here is \( \text{Distance} = \text{Speed} \times \text{Time} \). If speed increases, the distance covered in a given time also increases. This indicates a direct relationship, not inverse proportion.

4. **Analyze the Third Statement**:
- **Use of Electricity and Electricity Bill**:
- If the use of electricity increases, the electricity bill also increases. This is another example of a direct relationship, not inverse proportion.

5. **Conclusion**:
- The only statement that shows inverse proportion is the first one: **Number of Workers and Time Taken to Complete Work**.

### Final Answer:
- The statement that shows inverse proportions is: **Number of Workers and Time Taken to Complete Work**.

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