IGCSE · 4MA1 · Topic

Ratio Toolkit: past paper questions & worked solutions

Every Ratio Toolkit question from the 4MA1 papers in our bank, 2020–2026, sorted from easiest to hardest. Try each one first, then open the worked solution.

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14questions

55marks in total

26%of papers (14 of 54) include it

0/11/3easy / medium / hard

Questions, easiest first

Level is estimated from marks: 1–2 easy, 3–4 medium, 5+ hard.

1. Nov 2023 P2H · Q5

Medium3 marks

Nov 2023 P2H Question 5 (3 marks): Ratio Toolkit – 5 Avril bakes a cake. She uses flour, butter and sugar such that weight of flour : weight of butter = 6 : 5 weight of butter : weight of sugar = 3 : 2 Avril uses 120 grams of sugar. Work out the weight of flour Avril use

Show worked solution

Butter sugar
Butter : sugar $=3:2$.
Split the ratio
Sugar is $120$ g, so
\[ 2\text{ parts}=120 \]
\[ 1\text{ part}=60 \]
\[ \text{butter}=3\times 60=180 \]
Flour butter
Flour : butter $=6:5$.
\[ 5\text{ parts}=180 \]
\[ 1\text{ part}=36 \]
\[ \text{flour}=6\times 36=216 \]

Final answer

$216$ grams

2. May 2023 P1H · Q1

Medium3 marks

May 2023 P1H Question 1 (3 marks): Ratio Toolkit – 1 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. (Total f

Show worked solution

The ratio is
\[ \text{Arjun}:\text{Simon}:\text{Kath}=2:5:8 \]
Simon scored more than Arjun
Simon scored $12$ more than Arjun.
\[ 5-2=3\text{ parts} \]
\[ 3\text{ parts}=12 \]
\[ 1\text{ part}=4 \]
Kath scored
\[ 8\times 4=32 \]

Final answer

$32$

3. Jan 2022 P1H · Q2

Medium3 marks

Jan 2022 P1H Question 2 (3 marks): Ratio Toolkit – 2 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 mone

Show worked solution

The ratio is
\[ \text{Danil} : \text{Gabriel} : \text{Hadley}=3:5:9 \]
Split the ratio
The difference between Gabriel and Hadley is
\[ 9-5=4 \text{ parts} \]
Split the ratio
These 4 parts are $196$ euros, so one part is
\[ 196 \div 4=49 \]
Danil has 3 parts
Danil has 3 parts:
\[ 3\times 49=147 \]

Final answer

Danil receives $147$ euros.

4. May 2021 P1H · Q4

Medium3 marks

May 2021 P1H Question 4 (3 marks): Ratio Toolkit – 4 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

Show worked solution

Ducks pigs
Ducks : pigs $=5:9$.
Split the ratio
There are $36$ pigs, so
\[ 9\text{ parts}=36 \]
\[ 1\text{ part}=4 \]
\[ \text{ducks}=5\times 4=20 \]
Chickens ducks
Chickens : ducks $=7:2$.
\[ 2\text{ parts}=20 \]
\[ 1\text{ part}=10 \]
\[ \text{chickens}=7\times 10=70 \]

Final answer

$70$

5. Jan 2020 P1HR · Q1

Medium3 marks

Jan 2020 P1HR Question 1 (3 marks): Ratio Toolkit – 1 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. $ (Total for Question 1 is 3 marks) 1 5

Show worked solution

The ratio is
\[ \text{Brendon} : \text{Asha} : \text{Julie} = 3:2:6 \]
Asha and Julie together have
\[ 2+6=8 \text{ parts} \]
These 8 parts are worth
These 8 parts are worth $\$36$, so one part is
\[ 36 \div 8=4.50 \]
Brendon has 3 parts
Brendon has 3 parts:
\[ 3 \times 4.50=13.50 \]

Final answer

Brendon receives $\$13.50$.

6. Nov 2025 P1H · Q6

Medium4 marks

Nov 2025 P1H Question 6 (4 marks): Ratio Toolkit – 6 Eli and Peta share $275 in the ratio 2 : 3 Eli gives 3 11 of his share to charity. Peta gives 0.32 of her share to charity. Work out the total amount that Eli and Peta give to charity. $ (Total for Question 6 is 4 mar

Show worked solution

The ratio is
\[ \text{Eli} : \text{Peta} = 2:3 \]
Split the ratio
There are 5 parts, so one part is
\[ 275 \div 5=55 \]
Eli gets
\[ 2 \times 55=110 \]
Peta gets
\[ 3 \times 55=165 \]
Eli gives
\[ \frac{3}{11}\times 110=30 \]
Peta gives
\[ 0.32\times 165=52.8 \]
Total given to charity
Total given to charity:
\[ 30+52.8=82.8 \]

Final answer

$82.8$.

7. Jun 2025 P2H · Q6

Medium4 marks

Jun 2025 P2H Question 6 (4 marks): Ratio Toolkit – 6 Pau, Sam and Tia share £240 in the ratios 3 : 4 : 5 Sam and Tia each give £10 of their share to Pau. Work out the ratios of the amounts of money that Pau, Sam and Tia now have. Give your answer in its simplest form.

Show worked solution

The original ratio is
\[ \text{Pau} : \text{Sam} : \text{Tia} = 3:4:5 \]
There are
\[ 3+4+5=12 \text{ parts} \]
Each part is
\[ 240 \div 12=20 \]
Split the ratio
So the original amounts are
\[ 60,\ 80,\ 100 \]
Sam gives 10 to Pau
Sam gives 10 to Pau and Tia gives 10 to Pau, so the new amounts are
\[ 80,\ 70,\ 90 \]
Divide by 10
Divide by 10:
\[ 80:70:90=8:7:9 \]

Final answer

The new ratio is $8:7:9$.

8. May 2025 4WM2H · Q7

Medium4 marks

May 2025 4WM2H Question 7 (4 marks): Ratio Toolkit – 7 Pau, Sam and Tia share £240 in the ratios 3 : 4 : 5 Sam and Tia each give £10 of their share to Pau. Work out the ratios of the amounts of money that Pau, Sam and Tia now have. Give your answer in its simplest form.

Show worked solution

The original ratio is
\[ \text{Pau} : \text{Sam} : \text{Tia} = 3:4:5 \]
There are
\[ 3+4+5=12 \text{ parts} \]
Each part is
\[ 240 \div 12=20 \]
Split the ratio
So the original amounts are
\[ 60,\ 80,\ 100 \]
Sam gives 10 to Pau
Sam gives 10 to Pau and Tia gives 10 to Pau, so the new amounts are
\[ 80,\ 70,\ 90 \]
Divide by 10
Divide by 10:
\[ 80:70:90=8:7:9 \]

Final answer

The new ratio is $8:7:9$.

9. Jun 2023 P2H · Q5

Medium4 marks

Jun 2023 P2H Question 5 (4 marks): Ratio Toolkit – 5 Nancy has some coins with a total value of 85 pence. She has only 2 pence coins and 5 pence coins. The ratio number of 2 pence coins : number of 5 pence coins = 1 : 3 Nancy has more 5 pence coins than 2 pence coins. Ho

Show worked solution

Let the number of pence
Let the number of $2$ pence coins be $x$.
Split the ratio
Then the number of $5$ pence coins is $3x$.
Total value
Total value:
\[ 2x+5(3x)=85 \]
\[ 17x=85 \]
\[ x=5 \]
Split the ratio
So there are $5$ two-pence coins and $15$ five-pence coins.
\[ 15-5=10 \]

Final answer

$10$ more $5$ pence coins

10. Jan 2021 P1H · Q1

Medium4 marks

Jan 2021 P1H Question 1 (4 marks): Ratio Toolkit – 1 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 dol

Show worked solution

of the money is changed
$\frac{3}{10}$ of the money is changed to euros, so the rest is
\[ \frac{7}{10}\times 20160=14112 \]
Split the ratio
This rest is divided in the ratio
\[ \text{dollars} : \text{rupees} : \text{francs}=9:5:2 \]
There are
\[ 9+5+2=16 \text{ parts} \]
Split the ratio
The difference between dollars and francs is
\[ 9-2=7 \text{ parts} \]
Split the ratio
So the difference is
\[ \frac{7}{16}\times 14112=6174 \]

Final answer

$6174$ rand more is changed into dollars than francs.

11. Jan 2020 P2H · Q12

Medium4 marks

Jan 2020 P2H Question 12 (4 marks): Ratio Toolkit – 12 Astrid wants to buy some oil. She can buy the oil from either Dane Oil or Arctic Oil. Here is information about the price that each company will charge Astrid. Dane Oil Arctic Oil (4.2 × 105) litres for 2 500 000 Kron

Show worked solution

Convert standard form
Dane Oil costs $2500000$ Krone for
\[ 4.2\times 10^5=420000 \]
litres
litres.
\[ \text{Dane cost per litre}=\frac{2500000}{420000}=5.952\ldots \]
Convert standard form
So Dane Oil costs about $5.95$ Krone per litre.
Arctic Oil costs dollars. Convert
Arctic Oil costs $770000$ dollars. Convert this to Krone:
\[ 770000\times 6.57=5058900 \]
Arctic Oil gives
\[ 8.6\times 10^5=860000 \]
litres
litres.
\[ \text{Arctic cost per litre}=\frac{5058900}{860000}=5.882\ldots \]
Arctic Oil has the lower
Arctic Oil has the lower cost per litre.

Final answer

Arctic Oil

12. Jun 2026 P2HR · Q5

Hard5 marks

Jun 2026 P2HR Question 5 (5 marks): Ratio Toolkit – 5 Sarah and Dej each give some money to charity A and to charity B Sarah shares $400 between charity A and charity B in the ratio 2 : 3 Dej shares $375 between the two charities. He gives twice as much money to charity B

Show worked solution

Solution | Step 1
\[\text{Sarah to B}=400\times\frac{3}{2+3}=240\text{ dollars}.\]
Charity B receives 3 of the 5 equal shares.
Solution | Step 2
Dej gives to A and B in the ratio $1:2$, so \[\text{Dej to B}=375\times\frac{2}{3}=250\text{ dollars}.\]
Twice as much to B means that B receives 2 of the 3 shares.
Solution | Step 3
\[250-240=10\text{ dollars}.\]
Subtract the two donations to charity B.

Final answer

$\$10$ more.

13. Specimen 4WM2H · Q10

Hard5 marks

Specimen 4WM2H Question 10 (5 marks): Ratio Toolkit – 10 Payel makes 300 celebration cards. Birthday : anniversary : congratulations = 7 : 5 : 3. Two fifths of the birthday cards have numbers on them, 36% of the anniversary cards have numbers on them, and none of the congra

Show worked solution

The total number of parts
The total number of parts is
\[ 7+5+3=15 \]
Each part is
\[ 300\div 15=20 \]
Split the ratio
So the numbers of cards are:
\[ 140,\quad 100,\quad 60 \]
The birthday cards with numbers
The birthday cards with numbers are
\[ \frac25 \times 140=56 \]
The anniversary cards with numbers
The anniversary cards with numbers are
\[ 36\%\times 100=36 \]
Split the ratio
So the total with numbers is
\[ 56+36=92 \]
The fraction of all cards
The fraction of all cards is
\[ \frac{92}{300}=\frac{23}{75} \]

Final answer

$\frac{23}{75}$.

14. Jan 2020 P1H · Q5

Hard6 marks

Jan 2020 P1H Question 5 (6 marks): Ratio Toolkit – 5 120 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 g

Show worked solution

Split the ratio
Girls : boys $=3:5$, so there are $8$ parts.
\[ \text{girls}=120\times \frac38=45 \]
\[ \text{boys}=120\times \frac58=75 \]
Split the ratio
Boys climbing:
\[ \frac{16}{25}\times 75=48 \]
Split the ratio
Boys sailing:
\[ 75-48=27 \]
Split the ratio
For the girls, twice as many go sailing as climbing, so the girls are split in the ratio
\[ \text{sailing}:\text{climbing}=2:1 \]
Split the ratio
Girls sailing:
\[ \frac23\times 45=30 \]
Total sailing
Total sailing:
\[ 27+30=57 \]

Final answer

$57$

Ratio Toolkit: past paper questions & worked solutions

Questions, easiest first

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