Test: Ratio and Proportion - Year 7 MCQ

The ratio of the smaller bag to the larger bag is 3 : 4.
If the smaller bag holds 900 g (3 parts), let the larger bag hold x grams (4 parts).
Set up the proportion: 3/4 = 900/x.
Cross-multiply: 3x = 4 × 900 = 3600.
Solve: x = 3600/3 = 1200 g.
Thus, the larger bag holds 1,200 g.

The map scale is 1 cm = 8 km.
For a distance of 6.5 cm on the map, multiply by the scale factor: 6.5 × 8 = 52 km.
Thus, the distance is 52 km

The ratio of orange juice to lemonade is 3 : 7, meaning 3 parts orange juice to 7 parts lemonade.
If 60 ml of orange juice is used (3 parts), each part is 60/3 = 20 ml.
Lemonade is 7 parts, so 7 × 20 = 140 ml.
Alternatively, set up the proportion: 3/7 = 60/x.
Cross-multiply: 3x = 7 × 60 = 420, so x = 420/3 = 140 ml.
Thus, 140 ml of lemonade is needed.

To simplify the ratio 150 cm : 4 m, first convert 4 m to centimeters: 4 m = 400 cm.
The ratio becomes 150 : 400.
Divide both by their greatest common factor, 50: 150 ÷ 50 = 3, 400 ÷ 50 = 8.
Thus, the simplified ratio is 3 : 8.

The cost of 15 pints is £7.80, and we need the cost of 22 pints.
This is a direct proportion: 15/7.80 = 22/x.
Cross-multiply: 15x = 22 × 7.80 = 171.6.
Solve: x = 171.6/15 = 11.44 £.
Alternatively, the cost per pint is 7.80/15 = 0.52 £/pint, so 22 × 0.52 = 11.44 £.
Thus, the cost is £11.44.

To divide £85 in the ratio 1 : 4, calculate the total parts: 1 + 4 = 5.
Each part is 85/5 = 17 £.
The first part is 1 × 17 = 17 £, and the second part is 4 × 17 = 68 £.
Thus, the amounts are £17 : £68.

To divide 240 litres in the ratio 3 : 5, calculate the total parts: 3 + 5 = 8.
Each part is 240/8 = 30 litres.
The first part is 3 × 30 = 90 litres, and the second part is 5 × 30 = 150 litres.
Thus, the amounts are 90 : 150 litres.

The ratio of boys to girls is 3 : 4. With 12 boys (3 parts), each part is 12/3 = 4.
Girls = 4 parts: 4 × 4 = 16.
Alternatively, set up the proportion: 3/4 = 12/x.
Cross-multiply: 3x = 12 × 4 = 48, so x = 48/3 = 16.
Thus, there are 16 girls.

To simplify the ratio 12 kg : 4,800 g, convert 12 kg to grams: 12 kg = 12,000 g.
The ratio becomes 12,000 : 4,800.
Divide both by their greatest common factor, 2,400: 12,000 ÷ 2,400 = 5, 4,800 ÷ 2,400 = 2.
Thus, the simplified ratio is 5 : 2.

To simplify the ratio 8 : 12, divide both parts by their greatest common factor, 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3.
Thus, the simplified ratio is 2 : 3.