Edexcel IGCSE Maths
Topic questions Ratio, proportion and rates of change Ratio
59 questions · 246 marks · about 5 hours
Adam sells chocolate cakes and lemon cakes.
The ratio
number of chocolate cakes he sells: number of lemon cakes he sells 
5: 7
He sells 40 chocolate cakes.
Adam sells each chocolate cake for $8.50 He sells each lemon cake for $12.75
Work out the total amount of money Adam gets for selling the cakes.
Remy chooses one food item and one drink for his breakfast.
He can choose one food item from cereal (C) or fruit (F) or a pastry (P) He can choose one drink from milk (M) or juice (J) or tea (T)
Write down all the possible combinations that Remy can choose.
Ahmed and Bryn share some blueberries in the ratio 3: 4
What fraction of the blueberries does Bryn get?
Here is a list of ingredients needed to make 6 biscuits.
Asha makes some of these biscuits. She uses 450 g of flour.
How many biscuits does Asha make?
Julie makes 84 of these biscuits.
What weight of butter does Julie use?
Asha and Julie pay a total of 624 rupees for the ingredients. The ratio of the amount Asha pays to the amount Julie pays is 3: 5
How much does Julie pay?
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.
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.
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. He sells 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.
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. He sells 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.
Bilpa, Claudia and David share 1200 euros. Bilpa gets 
of the 1200 euros. Claudia gets 42% of the 1200 euros.
David gets the rest of the 1200 euros.
Given that
the amount of money Bilpa gets: the amount of money David gets = 1: n
work out the value of n
The pictogram gives information about the number of parcels a company posted on each of four days last week.
How many parcels were posted on Tuesday?
24 parcels were posted on Friday.
Show this information on the pictogram.
More parcels were posted on Wednesday than on Monday.
How many more?
Find the ratio
number of parcels posted on Monday: number of parcels posted on Thursday Give your answer in its simplest form.
Also involves Forming and solving equations
9 3 kg of carrots and 5 kg of potatoes cost a total of 207 rand. 2 kg of the carrots cost 48 rand.
Work out the cost of 1 kg of potatoes.
Bella buys 150 football shirts for a total cost of 1800 dollars.
She gives 10% of the shirts to the local football team. Bella sells the rest of the shirts for g dollars each. She makes a total profit of 360 dollars.
Work out the value of g
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 uses.
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 uses.
Roland, Seiso and Tim share the total cost of buying a plot of land.
Roland and Seiso share some of the cost in the ratio 2: 5 Roland’s share of the cost is $1700
Tim’s share of the cost is $2150 more than Roland’s share.
Work out the total cost of buying the plot of land.
Also involves Forming and solving equations
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.
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.
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.
How many more?
Also involves Forming and solving equations
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.
How many more?
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.
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
Also involves Forming and solving equations
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
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.
In a field, there are 60 sheep and 24 cows.
Find the ratio of the number of sheep to the number of cows. Give your ratio in its simplest form.
In a barn, there are only white ducks and brown ducks. In the barn, the ratio number of white ducks: number of brown ducks = 3: 7
What fraction of the ducks in the barn are white?
Giles and Sarah share some bales of hay in the ratio 11: 4
Sarah receives 20 bales of hay.
Work out how many bales of hay are shared in total.
Last season, Alisha and Jaya scored goals for their team in the ratio 4: 7 Jaya scored 39 more goals than Alisha.
Work out the number of goals Alisha scored.
Kim spends $ N
Of this, she spends
40% on food
and the rest on petrol
Kim spends $P on petrol.
Work out the ratio P:N in the form a:b where a and b are integers. Give your answer in its simplest form.
In November, Andre received a monthly salary of 2500 euros.
Of this he spent
40% on his rent 300 euros on leisure
The rest of Andre’s monthly salary was spent on household bills and on food where
the amount spent on household bills: the amount spent on food = 3: 7
Work out how much of his November monthly salary Andre spent on food.
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.
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.
Write the ratio 42: 96 in its simplest form.
There are only apples and pears in a fruit basket so that
the number of apples: the number of pears = 4: 11
What fraction of the fruit in the basket is pears?
Also involves Probability
A bag contains only pink sweets, white sweets, green sweets and red sweets.
The table gives each of the probabilities that, when a sweet is taken at random from the bag, the sweet will be green or the sweet will be red.
| Sweet | pink | white | green | red |
| Probability | 0.2 | 0.35 |
The ratio number of pink sweets: number of white sweets = 2: 1
There are 28 red sweets in the bag.
Work out the number of white sweets in the bag.
The table shows the average number of spectators per match, for each of six Spanish football teams, in one season.
| Team | Average number of spectators per match |
| Real Betis | 46 393 |
| Valencia | 38699 |
| Barcelona | 65731 |
| Athletic Bilbao | 37378 |
| Sevilla | 33069 |
| Real Madrid | 65027 |
Which team had the lowest average number of spectators per match?
Write the number 65 731 correct to the nearest thousand.
Write down the value of the 6 in the number 38 699
In one match, Sevilla played Valencia. In the match, Sevilla had 8 shots on target and Valencia had 12 shots on target.
Write the ratio 8:12 in its simplest form.
In the same match, Valencia had 72% possession of the ball.
Write 72% as a fraction in its simplest form.
Rose and Haydn share £250 in the ratio 2: 3
Rose gives all her share of the money to charity. Haydn gives 42% of his share of the money to charity.
Rose gives more money to charity than Haydn gives to charity.
Work out how much more.
Pieter owns a currency conversion shop.
Last Monday, Pieter changed a total of 20 160 rand into a number of different currencies. He changed 
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.
Pieter owns a currency conversion shop.
Last Monday, Pieter changed a total of 20 160 rand into a number of different currencies. He changed 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.
The people working for a company work in Team A or in Team B.
number of people in Team A: number of people in Team B = 3: 4 
of Team A work full time.
24% of Team B work full time.
Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.
Write 
as a fraction in its simplest form.
There are only blue bricks and white bricks in a box. The ratio of the number of blue bricks to the number of white bricks is 3: 7
What fraction of the bricks in the box are blue bricks?
There are 280 counters in a bag. 
of the counters are red. 
of the counters are yellow.
The rest of the counters are green.
Work out the number of green counters in the bag.
Alex makes 80 cakes to sell. He makes chocolate cakes, lemon cakes and fruit cakes where
number of number of number of:: = 3: 2: 5 chocolate cakes lemon cakes fruit cakes
Alex sells all of the chocolate cakes
The profit he makes on each cake he sells is shown in the table.
| Type of cake | Profit per cake he sells |
| chocolate | £2.00 |
| lemon | £1.70 |
| fruit | £2.40 |
Work out the total profit that Alex makes from the cakes he sells.
17Here is a list of ingredients needed to make apple crumble for 6 people.
Nadiya wants to make apple crumble for 14 people.
Work out the amount of butter she needs.
Alison makes apple crumble for a group of people.
She uses 630 g of oats.
Work out the number of people in the group.
At a cake sale, Michael sells some lemon cakes and some chocolate cakes.
the number of lemon cakes he sells: the number of chocolate cakes he sells = 2: 7
Michael sells a total of 162 cakes.
Work out the number of lemon cakes Michael sells.
Andreas, Isla and Paulo share some money in the ratios 3: 2: 5
The total amount of money that Isla and Paulo receive is £76 more than the amount of money that Andreas receives.
Andreas buys a video game for £48.50 with some of his share of the money.
Work out how much money Andreas has left from his share of the money when he has bought the video game.
Andreas, Isla and Paulo share some money in the ratios 3: 2: 5
The total amount of money that Isla and Paulo receive is £76 more than the amount of money that Andreas receives.
Andreas buys a video game for £48.50 with some of his share of the money.
Work out how much money Andreas has left from his share of the money when he has bought the video game.
Also involves Fractions
Write the ratio 32: 80 in its simplest form.
There are only red counters and blue counters in a bag. In the bag the number of red counters: the number of blue counters = 5: 7
What fraction of the counters in the bag are red?
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.
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.
Twice as many girls go sailing as go climbing.
Work out how many children go sailing on Sunday.
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.
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.
Twice as many girls go sailing as go climbing.
Work out how many children go sailing on Sunday.
In a box,
number of red buttons: number of blue buttons = 5: 3
number of blue buttons: number of green buttons = 1: 2
There are 48 green buttons in the box.
Work out the number of red buttons in the box.
Also involves Forming and solving equations
3 years ago, the ratio of Tom’s age to Clemmie’s age was 2: 7 Tom is now 15 years old and Clemmie is now x years old.
Find the value of x.
Also involves Forming and solving equations
A solid is made from a hemisphere and a cylinder. The plane face of the hemisphere coincides with the upper plane face of the cylinder.
The hemisphere and the cylinder have the same radius.
The ratio of the radius of the cylinder to the height of the cylinder is 1: 3
Given that the solid has volume 792
cm3 work out the height of the solid.
A football team played 55 games. Each game was won, drawn or lost.
number of games won: number of games drawn: number of games lost = 6: 3: 2
Work out how many more games the team won than the team lost.
The bar chart gives information about the total number of medals won by each of six countries at the 2016 Olympic Games.
Which of these countries won the fewest total number of medals?
Great Britain won 27 gold medals.
How many of the medals won by Great Britain were not gold medals?
Write down the ratio of the total number of medals won by Russia to the total number of medals won by Germany. Give your ratio in its simplest form.
The USA won 46 gold medals 37 silver medals 38 bronze medals
What fraction of the total number of medals won by the USA were gold medals?
There are some people in a cinema. 
of the people in the cinema are children. For the children in the cinema,
number of girls: number of boys = 2: 7
There are 170 girls in the cinema.
Work out the number of adults in the cinema.
There are some people in a cinema. 
of the people in the cinema are children. For the children in the cinema,
number of girls: number of boys = 2: 7
There are 170 girls in the cinema.
Work out the number of adults in the cinema.
Also involves Fractions
Anna and Lionel share $675 in the ratio 4: 5 Lionel gives 
of his share of the money to his mother.
How much money does Lionel give to his mother?
Also involves Fractions · Forming and solving equations
Each month Edna spends all her income on rent, on travel and on other living expenses.
She spends 
of her income on rent. She spends 
of her income on travel. She spends $420 of her income on other living expenses.
Work out her income each month.
Work out the difference between the largest share and the smallest share when 3450 yen is divided in the ratios 2: 6: 7
Work out the difference between the largest share and the smallest share when 3450 yen is divided in the ratios 2: 6: 7
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