Important Questions for Class 8 Maths Chapter 11 With Solutions

9. Which of the following quantities vary directly or indirectly with each other

1. Number of pens and their cost

2. Distance travelled (at constant speed) and petrol used.

3. Number of men available and time taken to do a job.

4. Area of land and its price.

5. wages y and hours of work x.

Solution:

1. As pens increase, cost increases – direct variation.

2. As distance travelled increases, the amount of petrol increases – direct variation.

3. Number of men decreases, time taken increases – Inverse variation.

4. Direct variation.

5. Direct variation.

10.  A 5m 60cm high vertical pole casts a shadow which is 3m 20cm long. Find at the same time

(i) length of the shadow cast by a different pole which is 10m 50cm high.

(ii) height of a pole which casts a shadow 5m long.

Solution:

Benefits of Solving Important Questions for Class 8 Maths Chapter 11

Improved Understanding of Key Concepts : By solving important questions, students gain a deeper understanding of how two quantities are related in direct and inverse proportions. They learn how changes in one quantity affect the other, whether they move in the same direction (direct proportion) or opposite directions (inverse proportion). This helps solidify the foundation of the concepts.

Mastery of Key Formulas : Solving these questions reinforces the understanding of the essential formulas for direct and inverse proportions.

Enhanced Problem-Solving Skills : Practicing different types of problems helps improve critical thinking and problem-solving abilities. Students learn how to approach and solve both simple and complex problems that involve direct or inverse relationships, which improves their logical and analytical skills.

Better Exam Preparation : Important questions are often similarly to those found in exams, helping students familiarize themselves with the question format. By solving these questions, students can identify common patterns and are better prepared to tackle similar questions during exams, ensuring a higher level of readiness.

Increased Confidence : Regular practice builds confidence in handling proportional relationships and using formulas effectively. Students become more comfortable with solving problems under time pressure, which helps reduce exam anxiety and improves overall performance.