Edexcel International GCSE Maths Ratio and Proportion Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Numbers and the Number System

Ratio and Proportion: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every ratio and proportion question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 11 questions worth 43 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

13 marksHigherJanuary 2020 · Paper 1HR (4MA1/1HR) · Q1

Brendon, Asha and Julie share some money in the ratios 3 : 2 : 6. The total amount of money that Asha and Julie receive is $36. Work out the amount of money that Brendon receives.

Show solution
  1. Asha and Julie together have 2 + 6 = 8 parts, and 8 parts = $36.
  2. 1 part = 36 ÷ 8 = $4.50
  3. Brendon has 3 parts: 3 × 4.50

Answer: $13.50

24 marksHigherJanuary 2021 · Paper 1H (4MA1/1H) · Q1

Pieter owns a currency conversion shop. Last Monday, Pieter changed a total of 20 160 rand into a number of different currencies. He changed 3⁄10 of the 20 160 rand into euros. He changed the rest of the rands into dollars, rupees and francs in the ratios 9 : 5 : 2. Pieter changed more rands into dollars than he changed into francs. Work out how many more.

Show solution
  1. Euros: 3⁄10 × 20 160 = 6048 rand
  2. The rest: 20 160 − 6048 = 14 112 rand
  3. 9 + 5 + 2 = 16 parts, so 1 part = 14 112 ÷ 16 = 882 rand
  4. Dollars have 9 parts and francs have 2 parts, a difference of 7 parts: 7 × 882

Answer: 6174 rand

33 marksHigherJune 2023 · Paper 1H (4MA1/1H) · Q1

Last season, the number of goals scored by Arjun, by Simon and by Kath for their football team were in the ratios 2 : 5 : 8. Simon scored 12 more goals than Arjun. Work out the number of goals scored by Kath.

Show solution
  1. Simon has 5 parts and Arjun has 2 parts, so the difference is 5 − 2 = 3 parts.
  2. 3 parts = 12 goals, so 1 part = 12 ÷ 3 = 4 goals.
  3. Kath has 8 parts: 8 × 4

Answer: 32

43 marksHigherJanuary 2022 · Paper 1H (4MA1/1H) · Q2

Danil, Gabriel and Hadley share some money in the ratios 3 : 5 : 9. The difference between the amount of money that Gabriel receives and the amount of money that Hadley receives is 196 euros. Work out the amount of money that Danil receives.

Show solution
  1. Hadley has 9 parts and Gabriel has 5 parts, so the difference is 4 parts = 196 euros.
  2. 1 part = 196 ÷ 4 = 49 euros
  3. Danil has 3 parts: 3 × 49

Answer: 147 euros

55 marksHigherJune 2024 · Paper 1HR (4MA1/1HR) · Q3

Norberto sells white loaves of bread and brown loaves of bread. He sells a total of 200 loaves such that the number of white loaves sold : the number of brown loaves sold = 3 : 2. Norberto sells the white loaves for £1.50 each and the brown loaves for £1.75 each. 40% of the price of a white loaf is profit. 60% of the price of a brown loaf is profit. Work out Norberto’s total profit when he sells all 200 loaves.

Show solution
  1. Share 200 in the ratio 3 : 2. There are 3 + 2 = 5 parts, so 1 part = 200 ÷ 5 = 40.
  2. White loaves = 3 × 40 = 120 and brown loaves = 2 × 40 = 80.
  3. Profit on one white loaf = 40% of £1.50 = 0.4 × 1.50 = £0.60, so 120 white loaves give 120 × 0.60 = £72
  4. Profit on one brown loaf = 60% of £1.75 = 0.6 × 1.75 = £1.05, so 80 brown loaves give 80 × 1.05 = £84
  5. Total profit = 72 + 84

Answer: £156

63 marksHigherJune 2021 · Paper 1H (4MA1/1H) · Q4

On a farm there are chickens, ducks and pigs. The ratio of the number of chickens to the number of ducks is 7 : 2. The ratio of the number of ducks to the number of pigs is 5 : 9. There are 36 pigs on the farm. Work out the number of chickens on the farm.

Show solution
  1. Make the ducks the same in both ratios. Ducks are 2 in the first and 5 in the second; the LCM is 10.
  2. Chickens : ducks = 7 : 2 = 35 : 10, and ducks : pigs = 5 : 9 = 10 : 18
  3. So chickens : ducks : pigs = 35 : 10 : 18
  4. 18 parts = 36 pigs, so 1 part = 2
  5. Chickens = 35 × 2

Answer: 70

76 marksHigherJanuary 2020 · Paper 1H (4MA1/1H) · Q5

120 children go on an activity holiday. The ratio of the number of girls to the number of boys is 3 : 5. On Sunday, all the children either go sailing or go climbing. 16⁄25 of the boys go climbing. Twice as many girls go sailing as go climbing. Work out how many children go sailing on Sunday.

Show solution
  1. 3 + 5 = 8 parts, so 1 part = 120 ÷ 8 = 15. Girls = 45, boys = 75.
  2. Boys climbing = 16⁄25 × 75 = 48, so boys sailing = 75 − 48 = 27
  3. Girls: sailing : climbing = 2 : 1, so share 45 into 3 parts: climbing = 15, sailing = 30
  4. Total sailing = 27 + 30

Answer: 57

83 marksHigherJanuary 2023 · Paper 1H (4MA1/1H) · Q5

In a box, there are only green sweets, orange sweets and yellow sweets. There are 280 sweets in the box so that the number of green sweets : the number of orange sweets = 2 : 3 and the number of orange sweets : the number of yellow sweets = 1 : 5. Work out how many green sweets there are in the box.

Show solution
  1. Make the orange parts match: orange : yellow = 1 : 5 = 3 : 15
  2. So green : orange : yellow = 2 : 3 : 15, which is 20 parts.
  3. 1 part = 280 ÷ 20 = 14, so green = 2 × 14

Answer: 28

93 marksHigherJanuary 2023 · Paper 1HR (4MA1/1HR) · Q5

C grams of chocolate is shared in the ratios 2 : 5 : 8. The difference between the largest share and the smallest share is 390 grams. Work out the value of C.

Show solution
  1. Difference between the largest and smallest shares = 8 − 2 = 6 parts
  2. 6 parts = 390 g, so 1 part = 65 g
  3. Total = 2 + 5 + 8 = 15 parts: 15 × 65

Answer: C = 975

105 marksHigherJune 2020 · Paper 1HR (4MA1/1HR) · Q10

Alex makes 80 cakes to sell, where number of chocolate cakes : number of lemon cakes : number of fruit cakes = 3 : 2 : 5. Alex sells all of the chocolate cakes, 3⁄4 of the lemon cakes and 7⁄8 of the fruit cakes. The profit per cake sold is £2.00 for chocolate, £1.70 for lemon and £2.40 for fruit. Work out the total profit that Alex makes from the cakes he sells.

Show solution
  1. 3 + 2 + 5 = 10 parts, so 1 part = 80 ÷ 10 = 8 cakes. Chocolate = 24, lemon = 16, fruit = 40.
  2. Sold: 24 chocolate, 3⁄4 × 16 = 12 lemon, 7⁄8 × 40 = 35 fruit
  3. Profit: 24 × 2.00 = £48, 12 × 1.70 = £20.40, 35 × 2.40 = £84
  4. Total = 48 + 20.40 + 84

Answer: £152.40

115 marksHigherJune 2024 · Paper 1H (4MA1/1H) · Q14

The combined savings of Abel and Bahira are 15 435 dinars. The savings of Bahira are 45% more than the savings of Abel. The savings of Bahira are 3⁄2 times the savings of Chanda. Work out the savings of Chanda.

Show solution
  1. Let Abel’s savings be A. Bahira has 45% more, so Bahira = 1.45A.
  2. Together: A + 1.45A = 2.45A = 15 435
  3. A = 15 435 ÷ 2.45 = 6300 dinars (Abel)
  4. Bahira = 15 435 − 6300 = 9135 dinars
  5. Bahira = 3⁄2 × Chanda, so Chanda = Bahira ÷ 3⁄2 = 9135 × 2⁄3

Answer: 6090 dinars

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