Sharing in a ratio and ratio problems - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 30 exam-style questions on Sharing in a ratio and ratio problems for Edexcel GCSE Maths (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.

30 questions
1–5 marks each
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20 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

Ruth and Sanjay win £1458 in a quiz.
They share the money in the ratio 5 : 4.

How much money does each person get?

Model answer

5 + 4 = 9 parts
One part = 1458 ÷ 9 = £162
Ruth: 5 × 162 = £810
Sanjay: 4 × 162 = £648

Explanation

Divide the total by the number of parts (5 + 4 = 9) to find one part, then multiply by each number in the ratio. Check that the shares add up to the total: 810 + 648 = 1458. Dividing by 5 and by 4 separately is a common mistake.

Mark scheme

1 mark
M1 for \(1458 \div 9\) (= 162) or for \(\frac{5}{9} \times 1458\) or \(\frac{4}{9} \times 1458\)
1 mark
A1 for Ruth £810 and Sanjay £648
cao; correct answer with no working scores full marks

Question 2

3 marks

Amir and Beth share some money in the ratio 7 : 4.
Amir gets £86.25 more than Beth.

How much money do they share altogether?

Model answer

Difference = 7 − 4 = 3 parts
3 parts = £86.25, so 1 part = 86.25 ÷ 3 = £28.75
Total = 7 + 4 = 11 parts: 11 × 28.75 = £316.25

Explanation

The £86.25 is not a share - it is the difference between the shares, which is 7 − 4 = 3 parts. Once you know one part, multiply by the total number of parts. A common mistake is to divide £86.25 by 11.

Mark scheme

1 mark
P1 for recognising that the difference is 3 parts, e.g. \(86.25 \div 3\) (= 28.75)
1 mark
P1 for their one part × 11
1 mark
A1 for £316.25
cao; correct answer with no working scores full marks

Question 3

3 marks

Shop A in the UK sells olive oil in 2.5 litre tins for £18.75 each.
Shop B in France sells olive oil in 3 litre tins for 25.20 euros each.

The exchange rate is £1 = 1.15 euros.

In which shop is the olive oil better value?
You must show your working.

Model answer

Shop A: 18.75 ÷ 2.5 = £7.50 per litre
Shop B: 25.20 ÷ 3 = 8.40 euros per litre
8.40 ÷ 1.15 = £7.304... per litre
£7.30 < £7.50, so Shop B is better value.

Explanation

To compare value you need the same quantity (1 litre) in the same currency. Divide euros by the exchange rate to change them into pounds, or multiply pounds by it to change them into euros. A common mistake is to multiply 8.40 by 1.15, which gives a value that is too big.

Mark scheme

1 mark
M1 for a correct conversion, e.g. \(25.20 \div 1.15\) (= 21.91...) or \(18.75 \times 1.15\) (= 21.5625)
1 mark
M1 for comparable values, e.g. £7.50 and £7.30... per litre, or 8.625 euros and 8.40 euros per litre
oe, e.g. the cost of 7.5 litres in each shop, or litres per pound
1 mark
C1 for Shop B, with correct comparable figures
dependent on both M marks

Question 4

5 marks

Lily makes orange paint by mixing red paint and yellow paint in the ratio 2 : 3.
She needs 12 litres of orange paint.

Red paint is sold in 750 ml tins costing £4.85 each.
Yellow paint is sold in 500 ml tins costing £3.60 each.

Work out the least amount Lily must spend to buy enough red paint and yellow paint.

Model answer

2 + 3 = 5 parts, 1 part = 12 ÷ 5 = 2.4 litres
Red = 2 × 2.4 = 4.8 litres; yellow = 3 × 2.4 = 7.2 litres
Red tins: 4.8 ÷ 0.75 = 6.4, so 7 tins
Yellow tins: 7.2 ÷ 0.5 = 14.4, so 15 tins
Cost = 7 × 4.85 + 15 × 3.60 = 33.95 + 54.00 = £87.95

Explanation

Share the 12 litres in the ratio 2 : 3, then work out how many tins of each colour are needed. Tins can only be bought whole, so 6.4 tins means 7 tins - rounding down would not give enough paint. Make sure the units match: 750 ml = 0.75 litres.

Mark scheme

1 mark
P1 for red = \(\frac{2}{5} \times 12\) (= 4.8 litres) or yellow = \(\frac{3}{5} \times 12\) (= 7.2 litres)
correct answer with no working scores full marks
1 mark
P1 for \(4.8 \div 0.75\) (= 6.4) and rounding up to 7 tins of red
ft their amount of red
1 mark
P1 for \(7.2 \div 0.5\) (= 14.4) and rounding up to 15 tins of yellow
ft their amount of yellow
1 mark
P1 for \(7 \times 4.85 + 15 \times 3.60\)
ft their whole numbers of tins
1 mark
A1 for £87.95
cao

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