RD Sharma Solutions for Class 8 Maths - Direct and Inverse variations - Free PDF Download
FAQs on RD Sharma Class 8 Maths Solutions Chapter 10 - Direct and Inverse variations
1. How do Vedantu’s RD Sharma Solutions for Class 8 Maths Chapter 10 help in understanding Direct and Inverse Variations?
Vedantu's RD Sharma Solutions for Class 8 Maths Chapter 10 provide step-by-step explanations for every problem in the textbook. This helps you understand the correct methodology for identifying whether quantities are in direct or inverse proportion and how to apply the formulas accurately. Each solution is crafted by experts to clarify complex concepts and build a strong foundation for exams.
2. What is the fundamental difference between direct and inverse variation as covered in this chapter?
The fundamental difference lies in how two quantities relate to each other:
- In direct variation, if one quantity increases, the other quantity also increases at the same rate (e.g., more workers finish more work). The ratio x/y remains constant.
- In inverse variation, if one quantity increases, the other quantity decreases proportionally (e.g., more workers take less time to finish the same job). The product x*y remains constant.
3. What types of problems are solved in the RD Sharma Class 8 Chapter 10 solutions?
The RD Sharma solutions cover a wide range of problems involving direct and inverse variations. This includes:
- Calculating unknown values in a proportion.
- Word problems related to time, work, speed, and distance.
- Questions involving mixtures and consumption.
- Multi-step problems where you first need to identify the type of variation.
4. Why is finding the 'constant of proportionality' (k) a crucial step in solving variation problems?
Identifying the constant of proportionality (k) is crucial because it represents the fixed relationship between the two variable quantities. In direct variation (y = kx) or inverse variation (xy = k), 'k' is the value that connects them. Once you calculate 'k' using a known pair of values, you can use it to find any unknown value in the problem, making it the fundamental key to the solution.
5. How can I identify whether a word problem involves direct or inverse variation?
To identify the type of variation, use a simple logical test. Ask yourself: "If I increase the first quantity, what will happen to the second quantity?"
- If the second quantity also increases (e.g., more articles, higher cost), it is a case of direct variation.
- If the second quantity decreases (e.g., more speed, less time), it is a case of inverse variation.
6. What is a common mistake students make when solving questions on inverse variation?
A common mistake is setting up the proportion incorrectly. For direct variation, we use x₁/y₁ = x₂/y₂, but for inverse variation, the relationship is x₁y₁ = x₂y₂. Students often forget this and use the direct variation formula for all problems, leading to incorrect answers. The RD Sharma solutions consistently highlight the correct formula for each problem type to help prevent this error.
7. Can you give a real-life example of inverse variation, apart from speed and time?
A great real-life example of inverse variation is the relationship between the number of people sharing a pizza and the size of the slice each person gets. If you increase the number of people sharing the same pizza, the size of each person's slice will decrease. Here, the product of the number of people and the slice size remains constant (equal to one whole pizza).
