Proportions & conversions
13 free practice questions with explanations
PassNova has 13 free Numerical Reasoning Test practice questions on Proportions & conversions, each with a clear explanation. Practise them in the browser with instant feedback — 100% free, no sign-up, on any device. Updated for 2026.
Proportions & conversions: example questions & answers
13 worked examples with answers and explanations below. Practise them in the browser with instant feedback on every answer.
A currency converts at £1 = €1.15. How many euros do you get for £400?
- A€500
- B€440
- C€460✓
- D€480
Answer: £400 × 1.15 = €460.
A map uses a scale of 1:50,000. A road measures 6 cm on the map. What is its real length in kilometres?
- A6 km
- B5 km
- C2 km
- D3 km✓
Answer: 6 cm × 50,000 = 300,000 cm = 3,000 m = 3 km.
If 8 identical pens cost £6.00, how much do 20 of the same pens cost?
- A£12.00
- B£15.00✓
- C£13.50
- D£16.00
Answer: One pen costs £0.75; 20 × £0.75 = £15.00.
Convert 2.5 kilograms into grams.
- A2,500 g✓
- B25,000 g
- C250 g
- D2,050 g
Answer: 1 kg = 1,000 g, so 2.5 kg = 2,500 g.
A car travels 45 miles. Given 1 mile is about 1.6 km, what is this distance in kilometres?
- A76 km
- B72 km✓
- C64 km
- D68 km
Answer: 45 × 1.6 = 72 km.
A recipe for 4 people needs 600 g of rice. How much rice is needed for 10 people?
- A1,500 g✓
- B1,200 g
- C1,600 g
- D1,400 g
Answer: Per person = 600 ÷ 4 = 150 g; 150 × 10 = 1,500 g.
$1 = £0.78. A product costs $250. What is the cost in pounds?
- A£200
- B£185
- C£190
- D£195✓
Answer: $250 × 0.78 = £195.
A 1.5-litre bottle is shared equally into glasses of 250 ml each. How many full glasses can be poured?
- A4
- B5
- C6✓
- D7
Answer: 1.5 litres = 1,500 ml; 1,500 ÷ 250 = 6 glasses.
It takes 3 workers 8 hours to complete a task. Assuming the same rate, how long would 4 workers take?
- A7 hours
- B5 hours
- C6 hours✓
- D6.5 hours
Answer: Total work = 3 × 8 = 24 worker-hours; 24 ÷ 4 = 6 hours.
A fertiliser is mixed with water in the ratio 1:25 by volume. How much fertiliser is needed to make 13 litres of mixture?
- A0.4 litres
- B0.5 litres✓
- C0.52 litres
- D0.65 litres
Answer: Total parts = 26; fertiliser = 1/26 of 13 litres = 0.5 litres.
On a plan drawn at 1:200, a room measures 4.5 cm by 3 cm. What is the real floor area in square metres?
- A27 m²
- B60 m²
- C90 m²
- D54 m²✓
Answer: Real dimensions = 9 m by 6 m (each cm = 2 m); area = 9 × 6 = 54 m².
€1 = £0.85 and £1 = $1.30. How many dollars is €500 worth (to the nearest dollar)?
- A$663
- B$765
- C$543
- D$553✓
Answer: €500 = £425 (×0.85), then £425 × 1.30 = $552.50, about $553.
A 6 cm by 8 cm photo is enlarged so the 6 cm side becomes 15 cm. What is the new length of the 8 cm side?
- A20 cm✓
- B22 cm
- C18 cm
- D24 cm
Answer: Scale factor = 15 ÷ 6 = 2.5; 8 × 2.5 = 20 cm.