Mathematics 0580 · IGCSE
Ratio and proportion
100 practice questions on Ratio and proportion, with worked solutions and instant marking.
$y$ is inversely proportional to $x^2$. If $x = 5$, then $y = 16$.
Feb/March 2017
Mrs Singh and Mr Patel work as teachers. They bring their two classes to the theatre to watch a play.
Feb/March 2017
For a holiday in India, the Smith family paid $5635$. This total was split in the ratio travel : accommodation : entertainment = 10 : 17 : 8.
Feb/March 2017
Divide 120 in the ratio 1 : 2.
Feb/March 2018
Write the information as a ratio in its simplest form.
Feb/March 2019
Amol and Priya split 645 parcels in the ratio Amol : Priya = 11 : 4.
Feb/March 2019
The bag has only red marbles, green marbles and blue marbles. The ratio of the counts of the three colours is red : green : blue = $12 : 5 : 2$. The number of red marbles is 112 greater than the number of green marbles.
Feb/March 2020
Sahil and Anika divide $78$ in the ratio $5 : 8$.
Feb/March 2021
Sahil and Anika divide $78$ in the ratio $5 : 8$.
Feb/March 2021
Joseph uses $\frac{5}{24}$ of his one week’s earnings to buy a jacket. The jacket costs $56.50$.
Feb/March 2021
Prakash purchases 45 flowers from a shop.
Feb/March 2021
To make 20 biscuits, the recipe needs 150 g flour, 125 g butter, and 50 g sugar.
Feb/March 2023
$y$ varies inversely with the square of $(x + 3)$. If $x = 5$, then $y = 0.375$.
Feb/March 2024
Xie converts 2000 dollars into krona. $1$ dollar $= 0.615$ euros. $1$ krona $= 0.087$ euros.
Feb/March 2025
Chi divides $480$ according to the ratio $2:3:7$. Find the size of the largest share.
Feb/March 2025
The combined mass of 38 spoons is 1824 g.
May/June 2015
Ahmed and Babar split $240\text{ g}$ of sweets in the ratio $7 : 3$.
May/June 2015
$p$ varies inversely with the square of $(q + 4)$. When $q = 2$, $p = 2$.
May/June 2015
Khamisi is aiming to attain the level needed to take part in an international athletics competition.
May/June 2015
On one day, 12000 vehicles pass through a road toll. The ratio of cars to trucks to motorcycles is 13 : 8 : 3.
May/June 2015
David travels to college by bus. The bus is late on 6 mornings out of 45. During one year, David travels to college by bus 180 times.
May/June 2016
The quantity $y$ varies directly with the positive square root of $x$. If $x = 9$, then $y = 12$.
May/June 2016
Work out the thickness of 250 sheets of paper.
May/June 2017
Since $h$ is directly proportional to the square root of $p$, $h = 5.4$ when $p = 1.44$.
May/June 2017
The quantity $y$ varies inversely with $\sqrt{1 + x}$. At $x = 8$, $y = 2$.
May/June 2017
Find the amount Soraya receives.
May/June 2018
$y$ varies directly with $(x - 1)^2$. At $x = 5$, $y = 4$.
May/June 2018
A car company employs three sales people: Anna, Mustapha and Joshua.
May/June 2018
Adele, Barbara and Collette divide $680 in the ratio 9 : 7 : 4.
May/June 2018
To make 20 biscuits, the ingredient list is: Butter: 260g Sugar: 500g Flour: 650g Rice: 425g
May/June 2018
Asif and Ben divide $2100 in the ratio Asif : Ben = 3 : 7.
May/June 2019
There are 22 coloured pencils in a box. Of these, 6 are pink, 9 are blue and 7 are yellow.
May/June 2019
Gerry and Alain each lap a running track. Gerry always needs 90 seconds for one complete circuit, whereas Alain always needs 105 seconds. They begin together from the same point.
May/June 2019
The variable $y$ is inversely proportional to the square root of $(x + 1)$. When $x = 8$, $y = 2$.
May/June 2019
A scale model of a car is drawn at $1 : 20$. The actual car has volume $12\text{ m}^3$.
May/June 2019
At a school, the music teacher assembles an orchestra. Within the orchestra, there are 36 string instruments, 15 woodwind instruments and 12 brass instruments.
May/June 2019
$y$ varies directly with the square root of $(x-3)$. If $x=28$, then $y=20$.
May/June 2021
Alex is constructing a house. The materials cost $1\frac{1}{2}$ times the land cost. The wages cost $1\frac{1}{4}$ times the land cost.
May/June 2021
Express the ratio $5 \times 10^{-1} : 2 : 3 \times 10^{1}$ in simplest form.
May/June 2022
Find the value of $y$ for $x = 124$.
May/June 2022
$y$ varies inversely with the cube of $(x - 1)$. $y = 9.45$ when $x = 3$.
May/June 2022
Kai and Ava each have a 57 cm-long piece of wood.
May/June 2023
$m$ varies inversely as the square of $(t + 2)$. When $t = 3$, $m = 0.64$.
May/June 2023
Antonio purchases a restaurant for $240000$. That sum represents $\frac{5}{8}$ of the money he has set aside to spend.
May/June 2023
Complete the statement for the value of $l$.
May/June 2023
Out of 30 students in the class, 13 go to school by bus. The school has 570 students in total.
May/June 2024
A piece of land is split in the ratio park : gardens : playground = $11 : 2 : 3$. The park’s area is $4620\text{ m}^2$.
May/June 2024
State the ratio apple juice : mango juice in simplest form.
May/June 2024
There are 70 students taking one of French, Spanish and German. The ratio of the number who study French to the number who study Spanish is 3 : 7. 15 students take French.
May/June 2025
This gives $y \propto \frac{1}{\sqrt{x}}$.
May/June 2025
To make 10 cakes, Tom requires 225 g of flour. Flour is sold by the shop in 500 g bags.
May/June 2025
Write the ratio of money invested by Anil : money invested by Baz in simplest form.
May/June 2025
The masses of box A and box B are in the ratio 4 : 7. Box B has a mass that is 2.4 kg greater than the mass of box A.
May/June 2025
Pip and Ali divide $785$ in the ratio Pip : Ali = $4 : 1$.
Oct/Nov 2015
Jason is given some birthday money. He uses $\frac{11}{15}$ of it and is left with $\$14.40$.
Oct/Nov 2015
$V$ varies directly as the cube of $(r + 1)$. When $r = 1$, $V = 24$.
Oct/Nov 2015
Pip and Ali divide $785 in the ratio Pip : Ali = $4 : 1$.
Oct/Nov 2015
$y$ varies inversely as $(x + 2)^2$. When $x = 1$, $y = 2$.
Oct/Nov 2015
In a film, a company employs 512 actors. Their numbers are split in the ratio men : women : children = 7 : 11 : 14.
Oct/Nov 2015
$y$ varies directly with the square root of $(x + 2)$. When $x = 7$, $y = 2$.
Oct/Nov 2016
Ralf and Susie divide $57$ in the ratio $2:1$.
Oct/Nov 2016
Calculate the least amount Tariq could pay for 5 litres of orange juice. Show your reasoning.
Oct/Nov 2016
A list of ingredients for making 18 chocolate chip biscuits is shown below.
Oct/Nov 2016
For a jigsaw puzzle, the edge pieces and the inside pieces are in the ratio $3 : 22$.
Oct/Nov 2016
From a survey of 40 workers, 6 cycle to the office. The office employs 800 workers altogether.
Oct/Nov 2017
$y$ varies inversely with $(x+1)^{2}$. $y = 50$ when $x = 0.2$.
Oct/Nov 2017
State the ratio of Alex’s money to Bobbie’s money in simplest form.
Oct/Nov 2017
Split $72$ in the ratio $5 : 4$.
Oct/Nov 2018
y varies directly with the square root of x. If $x = 9$, then $y = 6$.
Oct/Nov 2018
Divide 518 in the ratio $2:5$.
Oct/Nov 2019
To make 12 pancakes, you will need these ingredients: 110 g flour, 2 eggs, 200 ml milk, 50 g butter.
Oct/Nov 2019
$y$ varies inversely with $x^2$. When $x = 4$, $y = 2$.
Oct/Nov 2019
$t$ varies inversely with the square of $(x + 1)$. If $x = 2$, then $t = 5$.
Oct/Nov 2019
Mohsin’s farm has 600 pear trees together with 720 apple trees.
Oct/Nov 2019
Alan and Beth divide $\$1190$ in the ratio Alan : Beth = $5 : 2$.
Oct/Nov 2020
Alex and Chris divide sweets in the ratio Alex : Chris = 7 : 3, and Alex gets 20 more sweets than Chris.
Oct/Nov 2020
The sweets are divided between Alex and Chris in the ratio Alex : Chris $= 7 : 3$. Alex gets 20 more sweets than Chris.
Oct/Nov 2020
A scale model of a statue is 4 cm tall. Its volume is $12\text{ cm}^3$. The statue itself has a volume of $40500\text{ cm}^3$.
Oct/Nov 2020
$y$ varies inversely with the square root of $x$. If $y = 7$, then $x = 2.25$.
Oct/Nov 2020
Work out the ratio of First Class seats to Premium seats to Economy seats. State your answer in its simplest form.
Oct/Nov 2020
$y$ varies inversely with the square root of $(x - 2)$. For $x = 4.25$, $y = 12$. Determine $x$ when $y = 3$.
Oct/Nov 2021
Find the ratio Jo’s money : Mo’s money. Write your answer in its simplest form.
Oct/Nov 2021
Share $\$200$ in the ratio $7:3$.
Oct/Nov 2022
In a survey of 1200 people, 150 were left-handed.
Oct/Nov 2022
Divide $200$ so that it is shared in the ratio $7 : 3$.
Oct/Nov 2022
$y$ varies in proportion to the square of $(x - 7)$. If $x = 12$, then $y = 2$.
Oct/Nov 2022
These are the ingredients required for a pasta bake that serves 12 people. 250 g butter 600 g pasta 460 g mushrooms 280 g cheese 800 ml milk
Oct/Nov 2022
$F$ varies directly with the product of $m$ and $a$.
Oct/Nov 2023
Elize, Lily and Marco establish a business.
Oct/Nov 2023
This table presents details of several planets in the solar system: Planet | Diameter (km) | Average distance from the Sun (km) Earth | 12 800 | $1.496 \times 10^8$ Mars | 6 800 | $2.279 \times 10^8$ Jupiter | 143 000 | $7.786 \times 10^8$ Saturn | 120 500 | $1.434 \times 10^9$ Neptune | 49 500 | $4.495 \times 10^9$
Oct/Nov 2023
Safia has a length of fabric measuring 5.6 m. She divides it into two sections whose lengths are in the ratio $3:4$. Calculate the length of the longer part.
Oct/Nov 2024
$y$ varies directly with the square root of $x + 1$. $y = 10.5$ when $x = 8$.
Oct/Nov 2024
As $y$ varies inversely with $\sqrt{x + 2}$, the pair of values given is $x = 2$ and $y = 3$.
Oct/Nov 2024
A group of students sit a test. 75 of them pass the test. This represents $\frac{3}{5}$ of the students who sit the test.
Oct/Nov 2025
For chocolate cookies, the recipe makes 12. Ingredients: 100 g flour, 55 g butter, 55 g sugar, 20 g cocoa, 1 egg.
Oct/Nov 2025
The sum $n is divided between three sisters in the ratio 10 : 3 : 2. The smallest portion is $120.
Oct/Nov 2025
Kai, Jo and Liz divide some money in the ratio Kai : Jo : Liz = 4 : 7 : 13, and Jo is given $1400.
Oct/Nov 2025
Express this as the ratio 1 : n.
Oct/Nov 2025
Divide $90$ into the ratio $2:3$.
Oct/Nov 2025
Anna and Bruno divide some money in the ratio Anna : Bruno = 3 : 7. Bruno gets $36 more than Anna.
Oct/Nov 2025