Edexcel GCSE Maths (1MA1), Higher tier · Ratio, proportion and rates of change
Practise Ratio. 4 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy3 marks
In a class, the ratio of boys to girls is 3 : 5. Leah says, '\(\frac{3}{5}\) of the class are boys.'
(a) Explain why Leah is wrong.[1]
(b) There are 32 students in the class. How many of the students are girls?[2]
Show the answer and mark scheme
(a)Answer: The ratio compares boys with girls. There are \(3 + 5 = 8\) parts, so \(\frac{3}{8}\) of the class are boys.
C1 for explaining that there are 8 parts altogether, so the fraction of boys is \(\frac{3}{8}\)
Worked solution: 3 : 5 means 3 boys for every 5 girls, so 3 out of every 8 students are boys: \(\frac{3}{8}\), not \(\frac{3}{5}\).
(b)Answer: 20
M1 for \(32 \div 8\) (= 4) or \(\frac{5}{8} \times 32\)
A1 for 20
Worked solution: \(32 \div 8 = 4\), so there are \(5 \times 4 = 20\) girls.
Question 2Medium3 marks
Amir and Bea share some sweets in the ratio 5 : 3. Amir then gives Bea 12 of his sweets. Now they each have the same number of sweets.
How many sweets were there altogether?[3]
Show the answer and mark scheme
Answer: 96
P1 for recognising that the difference of 2 parts is \(2 \times 12 = 24\), or \(5k - 12 = 3k + 12\)
P1 for 1 part = 12 (or \(k = 12\))
A1 for 96
Worked solution: After the swap they are equal, so Amir had 24 more than Bea (he lost 12 and she gained 12). The difference is \(5 - 3 = 2\) parts, so 2 parts = 24 and 1 part = 12. Total \(= 8 \times 12 = 96\) sweets.
Question 3Hard3 marks
Anna, Ben and Cai share some money in the ratio 3 : 4 : 5. Cai then gives some of his money to Anna. Ben does not give or receive any money. The ratio Anna : Ben : Cai is now 5 : 4 : 3. Cai gave Anna £30.
How much money was shared?[3]
Show the answer and mark scheme
Answer: £180
P1 for recognising that one part is the same size in both ratios (12 parts in total each time, and Ben's 4 parts do not change)
P1 for Cai losing 2 parts = £30, so 1 part = £15
A1 for £180
Worked solution: Both ratios have \(3 + 4 + 5 = 12\) parts and the total is unchanged, so a part is worth the same amount before and after (Ben's 4 parts confirm this). Cai goes from 5 parts to 3 parts, so he gave 2 parts = £30, and 1 part = £15. Total \(= 12 \times 15 = 180\): £180 was shared (£45, £60, £75).