Ratio and Proportion

A recipe uses flour and sugar in the ratio 3:1. If you use 6 cups of flour, how much sugar do you need?

• A2 cups✓
• B3 cups
• C6 cups
• D1 cup

Answer: The ratio 3:1 means for every 3 parts flour, you need 1 part sugar. If flour is 6 cups, then sugar is 6 ÷ 3 = 2 cups.

A map scale is 1:1000. A distance of 5 cm on the map represents how many metres in real life?

• A50 metres✓
• B500 metres
• C50,000 metres
• D5,000 metres

Answer: If 1 cm on the map = 1,000 cm in real life, then 5 cm = 5 × 1,000 = 5,000 cm = 50 metres.

In a classroom, the ratio of boys to girls is 2:3. If there are 10 boys, how many girls are there?

• A10
• B12
• C15✓
• D20

Answer: The ratio 2:3 means for every 2 boys, there are 3 girls. If there are 10 boys, then 10 ÷ 2 = 5 groups, so there are 5 × 3 = 15 girls.

Which ratio is equivalent to 2:5?

• A8:15
• B4:10✓
• C3:7
• D6:20

Answer: 2:5 = 4:10 (multiply both by 2). Check: 2:5 = 2×2:5×2 = 4:10.

A painter mixes red and blue paint in the ratio 3:2. If he uses 9 litres of red paint, how much blue paint does he use?

• A6 litres✓
• B4 litres
• C9 litres
• D12 litres

Answer: The ratio 3:2 means for every 3 parts red, there are 2 parts blue. If red is 9 litres, then 9 ÷ 3 = 3 groups, so blue is 3 × 2 = 6 litres.

If 3 pens cost £1.50, what is the cost of 1 pen?

• A£0.50✓
• B£0.60
• C£0.40
• D£0.70

Answer: Cost of 1 pen = £1.50 ÷ 3 = £0.50.

A recipe serves 4 people and needs 200g of flour. How much flour is needed for 8 people?

• A200g
• B300g
• C100g
• D400g✓

Answer: 8 people is double 4 people, so you need double the flour: 200g × 2 = 400g.

What is the ratio 10:15 in its simplest form?

• A2:3✓
• B5:10
• C1:2
• D10:15

Answer: 10:15 can be simplified by dividing both by 5. 10÷5:15÷5 = 2:3.

If 5 apples cost £2, how much do 15 apples cost?

• A£4
• B£8
• C£10
• D£6✓

Answer: 15 apples is 3 times 5 apples, so the cost is 3 × £2 = £6.

A model car is made to a scale of 1:64. If the real car is 4 metres long, how long is the model car?

• A6.25 cm✓
• B6 cm
• C8 cm
• D5 cm

Answer: 4 metres = 400 cm. Model length = 400 ÷ 64 = 6.25 cm.

In a bag of sweets, the ratio of red to yellow is 3:2. If there are 15 red sweets, how many sweets are there in total?

• A20
• B25✓
• C30
• D35

Answer: Red:Yellow = 3:2. If red = 15, then 15 ÷ 3 = 5 groups. Yellow = 5 × 2 = 10. Total = 15 + 10 = 25.

Which ratio is in its simplest form?

• A3:6
• B2:4
• C4:5✓
• D6:9

Answer: 4:5 cannot be simplified further (they share no common factors). All others can be simplified: 2:4 = 1:2, 3:6 = 1:2, 6:9 = 2:3.

If 4 books cost £12, how much do 6 books cost?

• A£18✓
• B£20
• C£24
• D£15

Answer: Cost of 1 book = £12 ÷ 4 = £3. Cost of 6 books = 6 × £3 = £18.

A juice concentrate is mixed with water in the ratio 1:4. If you use 250 ml of concentrate, how much water do you use?

• A1,000 ml✓
• B1,250 ml
• C750 ml
• D500 ml

Answer: The ratio of concentrate to water is 1:4, so water = 250 × 4 = 1,000 ml.

A school has 300 pupils. The ratio of Y5 to Y6 pupils is 2:3. How many Y6 pupils are there?

• A100
• B120
• C150
• D180✓

Answer: There are 2 + 3 = 5 parts, so each part = 300 ÷ 5 = 60. Year 6 = 3 × 60 = 180 pupils.

If 3 apples cost £1.20, how much do 6 apples cost?

• A£3.20
• B£3.00
• C£2.80
• D£2.40✓

Answer: If 3 apples cost £1.20, then 6 apples (double the amount) cost £2.40.

A recipe for 4 people needs 200 g of butter. How much butter is needed for 8 people?

• A400 g✓
• B350 g
• C300 g
• D450 g

Answer: For 8 people (double), you need 200 × 2 = 400 g of butter.

The ratio of boys to girls in a class is 3:2. If there are 6 boys, how many girls are there?

• A3
• B4✓
• C5
• D6

Answer: If the ratio is 3:2 and there are 6 boys, then 6 ÷ 3 = 2 (scale factor). Girls = 2 × 2 = 4.

If 5 pens cost £3.50, how much do 10 pens cost?

• A£7.50
• B£6.50
• C£7.00✓
• D£8.00

Answer: 10 pens is double 5 pens, so the cost is £3.50 × 2 = £7.00.

A paint mixture uses red and blue in the ratio 2:3. If there are 10 litres of red paint, how much blue paint is needed?

• A10 litres
• B25 litres
• C20 litres
• D15 litres✓

Answer: Ratio 2:3 means for every 2 litres of red, there are 3 litres of blue. If red = 10, scale factor = 5, so blue = 3 × 5 = 15 litres.

A map scale is 1:100. If the distance on the map is 5 cm, what is the real distance?

• A50 m
• B5 km
• C5 m✓
• D500 m

Answer: 1:100 scale means 1 cm on map = 100 cm in reality. 5 cm = 500 cm = 5 m.

A recipe for 6 biscuits uses 120 g of sugar. How much sugar is needed for 12 biscuits?

• A260 g
• B200 g
• C180 g
• D240 g✓

Answer: For 12 biscuits (double), you need 120 × 2 = 240 g of sugar.

If 2 kg of oranges cost £4.00, what is the cost of 5 kg of oranges?

• A£9.00
• B£12.00
• C£8.00
• D£10.00✓

Answer: Cost per kg = £4 ÷ 2 = £2. For 5 kg: 5 × £2 = £10.

A ratio of red marbles to blue marbles is 4:5. If there are 20 red marbles, how many blue marbles are there?

• A20
• B24
• C25✓
• D30

Answer: Ratio 4:5: If red = 20, scale factor = 20 ÷ 4 = 5. Blue = 5 × 5 = 25.

If 3 notebooks cost £6, how much do 7 notebooks cost?

• A£12
• B£13
• C£15
• D£14✓

Answer: Cost per notebook = £6 ÷ 3 = £2. For 7 notebooks: 7 × £2 = £14.

A recipe uses flour and sugar in the ratio 3:1. If you use 150 g of flour, how many grams of sugar do you need?

• A30
• B50✓
• C60
• D75

Answer: The ratio 3:1 means 3 parts flour to 1 part sugar. One part = 150 ÷ 3 = 50 g, so the sugar is 50 g.

A map has a scale of 1:50,000. If two towns are 5 cm apart on the map, how far apart are they in reality?

• A250 km
• B25 km
• C2.5 km✓
• D5 km

Answer: 1:50,000 means 1 cm = 50,000 cm. 5 cm = 5 × 50,000 = 250,000 cm = 2.5 km.

In a class, the ratio of children with brown eyes to blue eyes is 5:2. If 10 children have brown eyes, how many have blue eyes?

• A2
• B3
• C4✓
• D5

Answer: Ratio 5:2: brown eyes = 10, scale factor = 10 ÷ 5 = 2. Blue eyes = 2 × 2 = 4.

If 4 litres of paint covers 32 square metres, how many litres are needed to cover 80 square metres?

• A12 litres
• B16 litres
• C8 litres
• D10 litres✓

Answer: Coverage per litre = 32 ÷ 4 = 8 m². For 80 m²: 80 ÷ 8 = 10 litres.

A recipe for 5 people needs 250 ml of milk. How much milk is needed for 10 people?

• A550 ml
• B400 ml
• C500 ml✓
• D450 ml

Answer: For 10 people (double), you need 250 × 2 = 500 ml of milk.