Ch 13 covers two types of proportional relationships: direct (both quantities increase or decrease together) and inverse (one increases as the other decreases). These concepts are essential for solving real-world problems.
Two quantities x and y are in direct proportion if x/y = k (constant). When one increases, the other increases proportionally. Example: more items → more cost (at fixed price per item). Formula: x₁/y₁ = x₂/y₂.
Two quantities x and y are in inverse proportion if xy = k (constant). When one increases, the other decreases proportionally. Example: more workers → less time to complete a job. Formula: x₁ × y₁ = x₂ × y₂.
Download: https://ncert.nic.in/textbook/pdf/hemh113.pdf | Complete book: https://ncert.nic.in/textbook/pdf/hemh1ps.zip
Direct: both increase or both decrease together (more books, more cost). Inverse: one increases while the other decreases (more speed, less time). Check: if x/y is constant → direct. If x×y is constant → inverse.
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