IGCSE · Practice questions · Ratio and proportion

One part, then the rest.

Six original Cambridge-style questions on ratio and proportion: simplifying, sharing, scaling and comparing value.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Find one part, then scale.

Same units before you simplify or compare.
Simplify by dividing every part by the highest common factor.
Share: add the parts, divide the total by that number, multiply back.
Difference given: the difference in parts matches the difference in amounts.
Proportion: find the value for one unit, then multiply; ask whether more of one means more or less of the other.

Recall

[2 marks]

Write each ratio in its simplest form. (a) $45 : 60$ (b) $2.4\ \text{m} : 80\ \text{cm}$

(a) HCF is 15: $3 : 4$ ✓
(b) $240\ \text{cm} : 80\ \text{cm} = 3 : 1$ ✓

Recall

[1 marks]

Write $5 : 8$ in the form $1 : n$.

Divide both parts by 5: $1 : 1.6$ ✓

Calculation

[2 marks]

Share $\$630$ in the ratio $2 : 3 : 4$.

$2 + 3 + 4 = 9$ parts; one part $= 630 \div 9 = \$70$. ✓
Shares: $\$140,\ \$210,\ \$280$. ✓

Calculation

[2 marks]

A map has scale $1 : 200\,000$. Two towns are 7.5 km apart. How far apart are they on the map, in centimetres?

$7.5\ \text{km} = 750\,000\ \text{cm}$. ✓
Map distance $= 750\,000 \div 200\,000 = 3.75$ cm. ✓

Analysis

[2 marks]

Pack A contains 400 g of cereal and costs $\$2.60$. Pack B contains 650 g and costs $\$4.10$. Which pack is better value? Show your working.

Pack A: $2.60 \div 4 = \$0.65$ per 100 g. ✓
Pack B: $4.10 \div 6.5 = \$0.631$ per 100 g (3 s.f.). ✓
Pack B is better value. ✓

Analysis

[3 marks]

Green paint is made by mixing blue and yellow paint in the ratio $2 : 7$. Tom has 1.5 litres of blue paint and 5 litres of yellow paint.

Work out the greatest amount of green paint he can make.

Using all the blue: 1 part $= 1.5 \div 2 = 0.75$ l, needing $7 \times 0.75 = 5.25$ l of yellow. He only has 5 l, so yellow runs out first. ✓
Using all the yellow: 1 part $= 5 \div 7$ l. ✓
Green paint $= 9 \times \dfrac{5}{7} = 6.43$ litres (3 s.f.). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.