PROPORTIONAL 3 REASONING–2 | Class 8 Mathematics Notes
By ConceptScroll Team · Published on 17 July 2026 · 3 min read
PROPORTIONAL 3 REASONING–2 – this guide gives you a concise, exam-ready overview of PROPORTIONAL 3 REASONING–2 from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
3.6 Inverse Proportions
This section introduces inverse proportion, where two quantities change in opposite directions such that their product remains constant. Unlike direct proportion where quantities increase or decrease together, in inverse proportion, if one quantity doubles, the other halves. For example, speed and travel time are inversely proportional for a fixed distance: as speed increases, time decreases. The product of speed and time equals the constant distance. Mathematically, if x and y are inversely proportional, then xy = k (constant). This is verified with examples like workers moving bricks, time taken by different modes of transport, and filling tanks with pumps. The section also includes problem-solving using the formula x1y1 = x2y2 and explains how to find unknown quantities. It highlights that when one quantity changes by a factor n, the other changes by 1/n. The section concludes with examples involving combined work, such as two people cutting vegetables together, demonstrating the use of inverse proportion and direct proportion concepts together.
📊 Diagram: See figure_14: Table showing speed and time for different transport modes; See figure_15: Graphical representation of inverse proportion; See figure_16: Illustration of inverse proportion formula; See figure_17: Work done by Ram and Shyam cutting vegetables together.
🧪 Activity: Students solve problems involving inverse proportion such as workers and days to complete work, pumps filling tanks, and combined work scenarios.
🔗 Connection: This section's understanding of inverse proportion complements earlier direct proportion concepts and prepares students for applying proportional reasoning in various real-life contexts.
Frequently asked questions
1. Which of the following pairs of quantities are in inverse proportion? (i) The number of taps filling a water tank and the time taken to fill it. (ii) The number of painters hired and the days needed to paint a wall of fixed size. (iii) The distance a car can travel and the amount of petrol in the tank. (iv) The speed of a cyclist and the time taken to cover a fixed route. (v) The length of cloth bought and the price paid at a fixed rate per metre. (vi) The number of pages in a book and the time required to read it at a fixed reading speed.
Answer: (i) Inverse proportion: More taps → less time to fill the tank. (ii) Inverse proportion: More painters → fewer days to paint. (iii) Direct proportion: More petrol → more distance. (iv) Inverse proportion: Higher speed → less time. (v) Direct proportion: More cloth → more price. (vi) Direct proportion: More pages → more time to read.
2. If 24 pencils cost ₹120, how much will 20 such pencils cost?
Solution: Cost of 24 pencils = ₹120 Cost of 1 pencil = 120 ÷ 24 = ₹5 Cost of 20 pencils = 20 × 5 = ₹100
3. A tank on a building has enough water to supply 20 families living there for 6 days. If 10 more families move in there, how long will the water last? What assumptions do you need to make to work out this problem?
Solution: Number of families initially = 20 Water lasts = 6 days New number of families = 20 + 10 = 30 Since more families → less days, quantities are inversely proportional. Let x = new number of days water will last. 20 × 6 = 30 × x 120 = 30x x = 120 ÷ 30 = 4 days Assumptions: Each family uses water at the same rate.
4. Fill in the average number of hours each living being sleeps in a day by looking at the charts. Select the appropriate hours from this list : 15, 2.5, 20, 8, 3.5, 13, 10.5, 18.
Answer depends on the charts provided in the textbook (not included here). Students should match each living being with the appropriate sleep hours from the given list.
Ready to ace this chapter?
Get the full PROPORTIONAL 3 REASONING–2 chapter — interactive notes, diagrams, worked solutions, polls and a free practice quiz — in the ConceptScroll app.
Study smarter with ConceptScroll
Daily NCERT-aligned reels, AI doubt solving and chapter quizzes — all free.
Start learning freeContinue reading
- Introduction to Graphs | Class 8 Mathematics Notes
Clear NCERT-aligned notes on Introduction to Graphs for Class 8 Mathematics.
- Introduction to Graphs | Class 8 Mathematics Notes
Clear NCERT-aligned notes on Introduction to Graphs for Class 8 Mathematics.
- Introduction to Graphs | Class 8 Mathematics Notes
Clear NCERT-aligned notes on Introduction to Graphs for Class 8 Mathematics.