Revision Notes for Class 8 Maths Chapter 10: Proportional Reasoning 2

Condensed revision notes for Class 8 Maths Chapter 10: Proportional Reasoning 2 – Ganita Prakash. These Class 8 Mathematics Chapter 10 notes are ideal for quick revision just before exams.

Last Updated: September 23, 2026

• Dividing a whole in a given ratio: each part’s share = (that part’s ratio number ÷ sum of all ratio numbers) × total quantity.
• Similar vs congruent: shapes with sides in the same ratio are similar (same shape), but only congruent if also the same actual size.
• Triangle inequality: a triangle can be constructed only if the sum of any two sides exceeds the third side.
• Pie chart angle for a category = (category count ÷ total count) × 360°. All angles in a pie chart always sum to 360°.
• Direct proportion: x/y = constant (both quantities increase or decrease together in the same ratio).
• Inverse proportion: x × y = constant (as one quantity increases, the other decreases proportionally). Test: check that x₁y₁ = x₂y₂ = x₃y₃… for every pair.
• Common inverse-proportion situations: number of workers vs. days to finish a job; number of taps vs. time to fill a tank; speed vs. time for a fixed distance; number of machines vs. days for a fixed output.
• Common direct-proportion situations: quantity bought vs. price paid (at a fixed rate); number of pages vs. time to read (at a fixed reading speed).
• Combined work rates: add individual rates (1/time for each) to find the combined rate; total time = 1 ÷ combined rate.
• Rule of thumb: always check with the product test (xy = constant) before assuming a relationship is inverse — don’t just guess from the wording.

More on this chapter: Solutions | Extra Questions | Class 8 Maths Book | Formulas Handbook

Frequently Asked Questions

What real-life situations are typically modelled using inverse proportion?
Situations such as the number of workers needed to complete a job in a given time, or the speed and time taken to cover a fixed distance, are typically modelled using inverse proportion, since increasing one factor reduces the other.

How is the unitary method connected to proportional reasoning?
The unitary method involves first finding the value of a single unit and then using that value to find the value of any required number of units, a practical technique built directly on the concept of proportion.

Written by Satish

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