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.
3.4 Dividing a Whole in a Given Ratio
This section explains how to divide a whole quantity into parts according to a given ratio, extending the method to ratios with multiple terms. For example, dividing 12 in the ratio 2:1 involves adding the terms (2 + 1 = 3), dividing the whole by this sum (12 ÷ 3 = 4), and multiplying each term by this quotient to get 8 and 4. For multi-term ratios like 1:1.5:3 used in concrete mixing, the sum of terms is 5.5. To make 110 units of concrete, divide 110 by 5.5 to get 20, then multiply each term by 20 to find quantities of cement, sand, and gravel (20, 30, and 60 units respectively). The general formula for dividing quantity x in ratio a:b:c:... is x × (a/(a+b+c+...)), x × (b/(a+b+c+...)), etc. The section also includes an example of constructing a triangle with angles in ratio 1:3:5 by dividing 180° accordingly. This method is widely applicable in practical situations requiring proportional division.
📊 Diagram: See figure_4: So, we need 20 units of cement, 30 units of sand, and 60 units of gravel to make the concrete.
🧪 Activity: Students practice dividing quantities like paint, concrete, or angles according to given ratios and construct triangles with angles in specified ratios.
🔗 Connection: The concept of dividing quantities in ratios sets the stage for understanding pie charts and proportional data representation in the next section.
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.
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