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Practise 28 exam-style questions on Sharing in a ratio and ratio problems 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.
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.
Share £72 in the ratio 5 : 3.
Total parts = 5 + 3 = 8
One part = 72 ÷ 8 = £9
5 × 9 = £45 and 3 × 9 = £27
Add the parts of the ratio to find how many equal shares there are, find the value of one share, then multiply. Check: 45 + 27 = 72.
M1 for 72 ÷ (5 + 3) (= 9)
correct answer with no working scores full marks
A1 for £45 and £27
cao
A cleaning solution is made by mixing 20 ml of concentrate with water to make 500 ml of solution.
How much concentrate is needed to make 1.5 litres of the solution?
1.5 litres = 1500 ml
1500 ÷ 500 = 3
Concentrate = 3 × 20 = 60 ml
The concentration stays the same, so the amount of concentrate is in proportion to the amount of solution. Change 1.5 litres to 1500 ml, which is 3 times 500 ml.
M1 for 1500 ÷ 500 (= 3) or 20 ÷ 500 × 1500
oe; correct answer with no working scores full marks
A1 for 60 (ml)
cao
In a choir, \(\dfrac{3}{8}\) of the members are men.
The rest of the members are women.
There are 20 more women than men.
How many members are in the choir?
Women = \(1 - \dfrac{3}{8} = \dfrac{5}{8}\) of the members, so men : women = 3 : 5.
The difference is 2 parts out of 8.
2 parts = 20, so 1 part = 10
Members = 8 × 10 = 80 (30 men and 50 women)
A part : whole fraction of \(\dfrac{3}{8}\) means the part : part ratio is 3 : 5. The difference of 20 is 2 parts, so one part is 10 and the whole choir is 8 parts.
M1 for women \(= \dfrac{5}{8}\) of the members, or men : women = 3 : 5
correct answer with no working scores full marks
M1 for \(\dfrac{2}{8}\) of the members = 20, or 2 parts = 20
A1 for 80
cao
18-carat gold contains gold and other metals in the ratio 3 : 1 by mass.
9-carat gold contains gold and other metals in the ratio 3 : 5 by mass.
A jeweller melts 40 g of 18-carat gold and 24 g of 9-carat gold together.
Find the ratio of gold to other metals in the new mixture.
Give your answer in its simplest form.
18-carat: 40 g shared 3 : 1; one part = 10 g
Gold 30 g, other metals 10 g
9-carat: 24 g shared 3 : 5; one part = 3 g
Gold 9 g, other metals 15 g
Total gold = 39 g, total other metals = 25 g
Ratio = 39 : 25 (39 and 25 have no common factor)
Split each alloy into its actual masses using its own ratio, then add the gold and add the other metals. 39 and 25 have no common factor, so 39 : 25 is already in its simplest form.
P1 for the 18-carat gold: 30 g gold and 10 g other metals
correct answer with no working scores full marks
P1 for the 9-carat gold: 9 g gold and 15 g other metals
P1 for the totals, 39 g gold and 25 g other metals
ft their amounts
A1 for 39 : 25
cao; 6 : 6 or 1 : 1 (adding the ratios) scores 0
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