Proportion as equality of ratios - Edexcel GCSE Maths (Non-calculator) Exam Questions

Practise 19 exam-style questions on Proportion as equality of ratios for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

19 questions
1–5 marks each
Instant marking
No sign-up needed

19 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

\((x + 2) : 6 = 5 : 3\)

Find the value of \(x\).

Model answer

\(\dfrac{x + 2}{6} = \dfrac{5}{3}\)
\(3(x + 2) = 30\)
\(x + 2 = 10\)
\(x = 8\)

Explanation

Write the equal ratios as equal fractions and cross-multiply, or notice that 6 is 2 × 3 so \(x + 2 = 2 \times 5 = 10\). Then solve the equation.

Mark scheme

1 mark
M1 for \(x + 2 = 10\), or \(3(x + 2) = 30\)
oe; correct answer with no working scores full marks
1 mark
A1 for \(x = 8\)
cao

Question 2

3 marks

\((2x - 1) : (x + 4) = 3 : 4\)

Find the value of \(x\).

Model answer

\(\dfrac{2x - 1}{x + 4} = \dfrac{3}{4}\)
\(4(2x - 1) = 3(x + 4)\)
\(8x - 4 = 3x + 12\)
\(5x = 16\)
\(x = 3.2\)

Explanation

Write the equal ratios as equal fractions and cross-multiply to remove the fractions. Expand the brackets carefully, then collect the \(x\) terms on one side.

Mark scheme

1 mark
M1 for \(4(2x - 1) = 3(x + 4)\)
oe; correct answer with no working scores full marks
1 mark
M1 for \(8x - 4 = 3x + 12\) leading to \(5x = 16\)
1 mark
A1 for \(x = 3.2\)
oe, e.g. \(\dfrac{16}{5}\)

Question 3

3 marks

Solution A is made by dissolving 15 g of salt in water to make 250 ml of solution.
Solution B is made by dissolving 24 g of salt in water to make 400 ml of solution.

Do the two solutions have the same concentration?
You must show how you get your answer.

Model answer

Solution A: 15 : 250 = 3 : 50
Solution B: 24 : 400 = 3 : 50
The ratios are equal, so yes, the solutions have the same concentration (60 g of salt per litre).

Explanation

Two mixtures have the same concentration when the ratio of salt to solution is the same. Simplify both ratios (or scale both to 1 litre) and compare.

Mark scheme

1 mark
M1 for simplifying or scaling one ratio, e.g. 15 : 250 = 3 : 50, or 0.06 g per ml
1 mark
M1 for the other, e.g. 24 : 400 = 3 : 50, or 0.06 g per ml
or 60 g per litre for both
1 mark
C1 for Yes, with correct supporting values

Question 4

4 marks

The instructions on a bottle of plant food say:
"Mix 30 ml of plant food with every 4 litres of water."

Kim has a 10 litre watering can and a 250 ml bottle of plant food.
Each time, she fills the watering can with 10 litres of water and adds the correct amount of plant food.

How many full cans can Kim make, and how much plant food will be left over?

Model answer

30 ml : 4 litres = \(p\) ml : 10 litres
10 ÷ 4 = 2.5, so \(p = 30 \times 2.5 = 75\) ml per can
3 cans use 3 × 75 = 225 ml; 4 cans would need 300 ml.
Kim can make 3 full cans with 250 − 225 = 25 ml left over.

Explanation

Keep the ratio of plant food to water the same: 10 litres is 2.5 times 4 litres, so she needs 2.5 times 30 ml in each can. Only whole cans count, so find how many lots of 75 ml fit into 250 ml and what remains.

Mark scheme

1 mark
P1 for a correct proportion, e.g. 30 : 4 = \(p\) : 10, or 7.5 ml per litre
correct answer with no working scores full marks
1 mark
P1 for 75 ml of plant food for each can
1 mark
P1 for 250 ÷ 75 = 3.33..., or 3 × 75 = 225
ft their amount per can
1 mark
A1 for 3 cans with 25 ml left over
both needed

Ready to try the rest? Every answer you write is marked against the mark scheme, so you can see exactly where the marks are.

AI Tutor Hints first, answers after you try

Hi! Stuck? Ask me for a hint and I’ll help you work it out. Once you’ve checked your answer I can explain exactly where the marks are.