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Class 8 Proportional Reasoning: Thinking Puzzles: cheat sheet
CBSE Computational Thinking and AI. Proportional reasoning shares in a ratio, mixes in the right amounts, scales maps and recipes, and tells direct from inverse proportion.
Key ideas
- To share in a ratio, divide the total by the sum of the parts, then multiply by each part.
- In a mixture, adding only water leaves the milk unchanged; work from the part that stays the same.
- Direct proportion: twice as much of one gives twice as much of the other, like a recipe or a map scale.
- Inverse proportion: more workers take fewer days; workers × days stays the same.
- Stacking puzzles are solved by trying every order and keeping those that follow all the rules.
Remember
| Share ₹600 in 1 : 2 : 3 | 600 ÷ 6 = 100 → ₹100, ₹200, ₹300 |
| Mixture | 20 L milk : water 3 : 1 → 15 L and 5 L; for 3 : 2 add 5 L of water |
| Inverse proportion | 6 workers × 10 days = 60 → 4 workers take 15 days |
| Map scale 1 cm : 5 km | 7 cm on the map = 35 km |
| Recipe | 300 g for 4 people → 450 g for 6 |
| Orders of 4 different blocks | 4 × 3 × 2 × 1 = 24 |
Watch out
- Dividing the total by one part instead of by the sum of the parts.
- Treating more workers as more days: that is inverse, not direct, proportion.
- Changing the milk when only water is added.
Worked example
Four blocks with a circle, a triangle, a square and a star are stacked one on top of another. (1) The triangle is immediately above the star. (2) The triangle is somewhere above the square. (a) How many different stacks follow all the rules? (b) How many follow all of them except rule (2)?
Working: all rules, from the top: circle/triangle/star/square; triangle/star/circle/square; triangle/star/square/circle
Answer: (a) 3; (b) 6
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