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NCERT Class 8 Maths Chapter 10

Proportional Reasoning-2

NCERT Class 8 Maths Chapter 10 (Ganita Prakash Part 2) extends proportional reasoning to inverse proportion and its applications. This CBSE chapter covers how to identify and solve problems where quantities are inversely related — when one increases, the other decreases proportionally. Real-world applications include speed-time problems, work-time problems, and resource allocation.

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Key Terms

Inverse Proportion
A relationship where two quantities are related such that when one increases, the other decreases in the same ratio; x × y = constant (k); e.g., speed and time for a fixed distance.
Direct Proportion
A relationship where two quantities increase or decrease together in the same ratio; y/x = constant; contrast with inverse proportion.
Constant of Variation
The constant product (for inverse proportion) or constant ratio (for direct proportion) that defines the proportional relationship.
Work and Time
A classic application of inverse proportion — if more workers are available, less time is needed to complete the same amount of work.
Speed, Distance, Time
A relationship governed by: Distance = Speed × Time. For fixed distance, speed and time are inversely proportional.
More-Less Type Problem
A problem-solving approach identifying whether more of one quantity means more or less of another, to determine if direct or inverse proportion applies.
Cross-Multiplication Method
A technique for solving proportion equations: if a/b = c/d, then ad = bc; used to find the unknown in both direct and inverse proportion problems.

Frequently Asked Questions

What is inverse proportion Class 8 Maths?▾

Two quantities are in inverse proportion when one increases as the other decreases in the same ratio. Their product remains constant: x × y = k. Examples: (1) More workers → less time to finish a job, (2) Higher speed → less time to cover a distance. If x₁y₁ = x₂y₂, the quantities are inversely proportional. NCERT Class 8 Chapter 10 covers this in depth.

What is the difference between direct and inverse proportion Class 8 NCERT?▾

In direct proportion, as one quantity increases, the other also increases (ratio constant: y/x = k). In inverse proportion, as one increases, the other decreases (product constant: xy = k). Direct: 'more of one → more of other' (e.g., more apples → more cost). Inverse: 'more of one → less of other' (e.g., more workers → less time).

How do you solve inverse proportion problems Class 8?▾

Step 1: Verify the quantities are inversely proportional (product is constant). Step 2: Set up x₁y₁ = x₂y₂. Step 3: Substitute known values and solve. Example: 4 workers take 12 days. How long for 6 workers? 4 × 12 = 6 × d; d = 48/6 = 8 days. As more workers are added, fewer days are needed — inverse proportion.

How is speed related to time by inverse proportion Class 8?▾

For a fixed distance, speed and time are inversely proportional: Speed × Time = Distance (constant). If you travel at twice the speed, you take half the time. If Speed₁ × Time₁ = Distance = Speed₂ × Time₂. Example: Travelling 120 km at 60 km/h takes 2 hours; at 40 km/h it takes 3 hours. 60×2 = 40×3 = 120.

How do you identify whether a problem is direct or inverse proportion Class 8?▾

Ask: 'If I have more of X, will I have more or less of Y (keeping everything else fixed)?' More X → More Y = Direct proportion. More X → Less Y = Inverse proportion. Examples: More distance at same speed → More time (Direct). More workers for same job → Less time (Inverse). More pipes filling a tank → Less time to fill (Inverse).

What are real-life examples of inverse proportion Class 8 Maths?▾

Real-life inverse proportion examples: (1) Speed and travel time (faster speed, less time), (2) Number of workers and days to complete a job, (3) Number of pipes and time to fill a tank, (4) Number of animals and days food stock lasts, (5) Gear size and rotation speed in a bicycle. All of these are covered or implied in NCERT Class 8 Maths Chapter 10.

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