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GCSE Maths Higher: Ratio and proportion practice questions
Ten free GCSE Maths Higher tier questions on direct and inverse proportion, reverse percentages, combining ratios, density, growth and similar shapes, each with a worked solution. Suitable for AQA, Edexcel and OCR.
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Timed mode
10 questions in 15 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.
विषय: Direct proportion
1. y is directly proportional to x². When x = 2, y = 12. Find y when x = 5.
हल
D. 75
- y = kx², so 12 = k × 4 and k = 3.
- When x = 5: y = 3 × 25 = 75.
विषय: Inverse proportion
2. y is inversely proportional to x. When x = 3, y = 8. Find y when x = 6.
हल
C. 4
- y = k/x, so 8 = k/3 and k = 24.
- When x = 6: y = 24/6 = 4.
विषय: Reverse percentages
3. After a 20% increase, a price is £84. What was the original price?
हल
B. £70
- The new price is 120% of the original: multiplier 1.2.
- 84 ÷ 1.2 = £70.
विषय: Combining ratios
4. x : y = 3 : 5 and y : z = 2 : 7. Find x : z.
हल
A. 6 : 35
- Make y the same in both: x : y = 6 : 10 and y : z = 10 : 35.
- So x : y : z = 6 : 10 : 35, and x : z = 6 : 35.
विषय: Density
5. A block has a mass of 600 g and a volume of 250 cm³. Find its density.
हल
D. 2.4 g/cm³
- Density = mass ÷ volume.
- 600 ÷ 250 = 2.4 g/cm³.
विषय: Compound units
6. Convert 72 km/h to metres per second.
हल
C. 20 m/s
- 72 km/h = 72 000 m in 3600 s.
- 72 000 ÷ 3600 = 20 m/s.
विषय: Growth
7. A population of 500 bacteria doubles every hour. How many are there after 4 hours?
हल
B. 8000
- After 4 hours: 500 × 2⁴.
- 500 × 16 = 8000.
विषय: Percentage change
8. A price falls from £250 to £190. Find the percentage change.
हल
A. 24% decrease
- Change = 250 − 190 = 60.
- Percentage change = 60 ÷ 250 × 100 = 24%, and it is a decrease.
विषय: Similar shapes
9. Two similar shapes have lengths in the ratio 1 : 3. What is the ratio of their areas?
हल
D. 1 : 9
- Area scale factor = (length scale factor)².
- 3² = 9, so 1 : 9.
विषय: Pressure
10. A force of 600 N acts on an area of 0.5 m². Find the pressure.
हल
C. 1200 Pa
- Pressure = force ÷ area.
- 600 ÷ 0.5 = 1200 Pa (N/m²).