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P6 maths ratio and proportion paper 3 (challenge): mixtures and inverse ratios
P6 maths ratio and proportion paper 3 (challenge): mixtures and inverse ratios
Ten challenge items: mixing ratios, perimeter back to sides, differences back to totals, scale and speed ratios.
Direct answers Find what one part stands for first, then answer what is asked; each item has a note in the answer table.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P6 Maths Ratio and Proportion |
| Level | P6 |
02 Questions (10 items)
- FoundationBottle A has juice to water 1 : 4 and bottle B 2 : 3, each holding 500 mL. They are mixed. What is the ratio of juice to water?
- FoundationA rectangle has length to breadth 7 : 4 and a perimeter of 88 cm. Find its length and breadth.
- FoundationIn an alloy the ratio of copper to zinc is 5 : 3 and the copper is 40 g heavier. What is the total mass?
- IntermediateWith a scale of 1 : 50000, how many centimetres on the map represent a real distance of 2.5 km?
- IntermediateThree numbers are in the ratio 3 : 4 : 5 and the largest exceeds the smallest by 24. Find the numbers.
- IntermediateA walks 300 m in 5 minutes and B walks 400 m in 4 minutes. Find the ratio of their speeds.
- ChallengeShare $1050 among three people in the ratio 2 : 3 : 5. How much does each get?
- ChallengeGiven A : B = 4 : 7 and B : C = 14 : 9, find A : C in simplest form.
- ChallengeMilk tea is made with milk to tea 3 : 10. With 60 mL of milk, how much milk tea can be made?
- Error redoA pupil joined A : B = 2 : 3 and B : C = 4 : 5 as 2 : 3 : 5. What is the correct A : B : C?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3 : 7 | A holds 100 mL juice and 400 mL water, B holds 200 mL and 300 mL, so the mixture is 300 : 700 = 3 : 7. |
| 2 | Length 28 cm and breadth 16 cm | Length plus breadth is 88 ÷ 2 = 44 cm over 11 parts, so one part is 4 cm, giving 28 cm and 16 cm. |
| 3 | 160 g | The difference is 5 − 3 = 2 parts = 40 g, so one part is 20 g and all 8 parts weigh 160 g. |
| 4 | 5 cm | 2.5 km is 250000 cm, and 250000 ÷ 50000 = 5 cm. |
| 5 | 36, 48 and 60 | The gap is 5 − 3 = 2 parts = 24, so one part is 12 and the numbers are 36, 48 and 60. |
| 6 | 3 : 5 | A covers 60 m per minute and B 100 m, and 60 : 100 simplifies to 3 : 5. |
| 7 | $210, $315 and $525 | There are 10 parts, 1050 ÷ 10 = 105 dollars each, giving 210, 315 and 525 dollars. |
| 8 | 8 : 9 | Make B equal to 14, so A : B = 8 : 14 and B : C = 14 : 9, giving A : C = 8 : 9. |
| 9 | 260 mL | 3 parts are 60 mL, so one part is 20 mL, the tea is 200 mL and the drink totals 260 mL. |
| 10 | 8 : 12 : 15 | B is 3 in one ratio and 4 in the other, so make it 12: 2 : 3 = 8 : 12 and 4 : 5 = 12 : 15, giving 8 : 12 : 15. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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