Ratio, Proportion & Rates of Change
12 free practice questions with explanations
PassNova has 12 free KS3 Maths practice questions on Ratio, Proportion & Rates of Change, each with a clear explanation. Practise them in the browser with instant feedback — 100% free, no sign-up, on any device. Updated for 2026.
Ratio, Proportion & Rates of Change: example questions & answers
12 worked examples with answers and explanations below. Practise them in the browser with instant feedback on every answer.
Divide 36 sweets between two people in the ratio 1 : 2. How many does the second person get?
- A12
- B18
- C24✓
- D36
Answer: 1 + 2 = 3 parts. Each part = 36 ÷ 3 = 12. The second person gets 2 parts = 24.
Simplify the ratio 10 : 15.
- A5 : 10
- B2 : 3✓
- C1 : 2
- D3 : 2
Answer: Divide both sides by their common factor 5: 10 : 15 = 2 : 3.
A car travels 120 km in 2 hours. What is its average speed?
- A60 km/h✓
- B240 km/h
- C30 km/h
- D120 km/h
Answer: Speed = distance ÷ time = 120 ÷ 2 = 60 km/h.
If 3 pens cost £1.20, how much do 5 pens cost?
- A£1.80
- B£2.40
- C£2.00✓
- D£1.50
Answer: One pen costs £1.20 ÷ 3 = £0.40, so 5 pens cost 5 × £0.40 = £2.00.
What is 4 : 2 written in the form n : 1?
- A8 : 1
- B4 : 1
- C2 : 1✓
- D1 : 2
Answer: Divide both sides by 2: 4 : 2 = 2 : 1.
A recipe for 4 people uses 200 g of rice. How much is needed for 6 people?
- A400 g
- B300 g✓
- C350 g
- D250 g
Answer: Per person = 200 ÷ 4 = 50 g. For 6 people = 6 × 50 = 300 g.
Increase £40 by 15%.
- A£6.00
- B£46.00✓
- C£34.00
- D£55.00
Answer: 15% of £40 is £6, and an increase means adding that on, so the new amount is £46.00. A quicker method is to multiply £40 by 1.15.
Decrease 250 by 12%.
- A220✓
- B280
- C238
- D30
Answer: 12% of 250 is 30, and a decrease means taking that away, which leaves 220. Subtracting 12 rather than 12% would leave 238.
The price of a jacket rises from £80 to £92. What is the percentage increase?
- A12%
- B13%
- C15%✓
- D87%
Answer: The rise is £92 - £80 = £12, and a percentage change is always measured against the original amount: 12 ÷ 80 × 100 = 15%. Dividing 80 by 92 instead gives about 87%, which is the calculation upside down.
A shop increases a price by 10%, then later decreases the new price by 10%. Compared with the original price, the final price is:
- Aunchanged
- B1% higher than the original
- C10% lower than the original
- D1% lower than the original price✓
Answer: Multiplying by 1.1 and then by 0.9 gives 0.99, so the final price is 99% of the original. The second 10% is taken off a bigger amount than the 10% that was added on, so the two changes do not cancel out.
A coach travels 150 km in 2.5 hours. What is its average speed?
- A375 km/h
- B60 km/h✓
- C37.5 km/h
- D75 km/h
Answer: Speed is distance divided by time: 150 ÷ 2.5 = 60 km/h. Dividing by 2 rather than 2.5 gives 75 km/h, and multiplying instead of dividing gives 375.
A block of metal has a mass of 240 g and a volume of 30 cm³. What is its density?
- A0.125 g/cm³
- B7200 g/cm³
- C8 g/cm³✓
- D270 g/cm³
Answer: Density is mass divided by volume: 240 ÷ 30 = 8 g/cm³. Dividing the volume by the mass gives 0.125, which is the calculation the wrong way round.