CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions1. Number1.9 Working with Ratios

Syllabus Edition

First teaching 2021

Last exams 2024

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1.9 Working with Ratios

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1
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Divide $24 in the ratio 7 : 5.
 

$ ................... , $ ...................

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2
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The fares for a train journey are shown in the table below.

From London to Marseille Standard fare Premier fare
Adult $84 $140
Child $60 $96

For the standard fare, write the ratio    adult fare : child fare    in its simplest form.
 

..................... : .....................

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3
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A plane has 14 First Class seats, 70 Premium seats and 168 Economy seats.

Find the ratio   First Class seats : Premium seats : Economy seats.
Give your answer in its simplest form.
 

............... : ............... : ...............

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4
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For a morning flight, the costs of tickets are in the ratio

First Class : Premium : Economy = 14 : 6 : 5.

The cost of a Premium ticket is $114.

Calculate the cost of a First Class ticket and the cost of an Economy ticket.

 

  First Class $ ................................................

Economy $ .................................................

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5
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Kristian and Stephanie share some money in the ratio 3 : 2.
Kristian receives $72.

Work out how much Stephanie receives.

 

$ ...............................................

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1
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Alex and Chris share sweets in the ratio    Alex : Chris = 7 : 3.
Alex receives 20 more sweets than Chris.

Work out the number of sweets Chris receives.

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2
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Arjun and Gretal each pay rent.

In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7.
In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 9 : 13.

Arjun paid the same amount of rent in both 2018 and 2019.
Gretal paid $290 more rent in 2019 than she did in 2018.

Work out the amount Arjun paid in rent in 2019.


$ ................................................

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3
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Some visitors to a campsite are in the ratio

men space colon space women equals 5 space colon space 4 and women space colon thin space children equals 3 space colon space 7.

i)

Calculate the ratio space men space colon thin space women space colon thin space children space in its simplest form.
 

................... : ................... : ................... [2]

ii)

There are 224 children at the campsite.

Calculate the total number of men and women.
 

[3]

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4
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One day Dhanu plays with his model railway from 06 50 to 11 15.
He then rides his bicycle for 3 hours.

Find the ratio t i m e space p l a y i n g space w i t h space m o d e l space r a i l w a y space colon space t i m e space r i d i n g space b i c y c l e.
Give your answer in its simplest form.


......................... : .........................

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5
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Ali and Mo share a sum of money in the ratio Ali : Mo = 9 : 7.
Ali receives $600 more than Mo.

Calculate how much each receives.

Ali $ ...................................................

Mo $ ...................................................

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6
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The fares for a train journey are shown in the table below.

From London to Marseille Standard fare Premier fare
Adult $84 $140
Child $60 $96

For one journey from London to Marseille, the ratio

number of adults : number of children = 11 : 2.
 

There were 220 adults in total on this journey.
All of the children and 70% of the adults paid the standard fare. 
The remaining adults paid the premier fare.

Calculate the total of the fares paid by the adults and the children.
 

$ .............................................

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7
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Some people who work for a company are in the following age groups.

Group A Group B Group C
Under 30 years 30 to 50 years Over 50 years


The ratio of the number in group A to the number in group B is  7 : 10.
The ratio of the number in group B to the number in group C is  4 : 3.

i)
Find the ratio of the number in group A to the number in group C.
Give your answer in its simplest form.


....................... : ....................... [3]

ii)
There are 45 people in group C.

Find the total number of people who work for the company.


[3]

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1
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The table shows the surface area of some countries and their estimated population in 2017.

Country Surface area (km2) Estimated population in 2017
Brunei 5.77 × 103 433 100
China 9.60 × 106 1 388 000 000
France 6.41 × 105 67 000 000
Maldives 3.00 × 102 374 600

The ratio       surface area of the Maldives : surface area of China can be written in the form   1 : n.

Find the value of n.


n space equals ................................................

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2a
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Mohsin has 600 pear trees and 720 apple trees on his farm.

Write the ratio pear trees : apple trees in its simplest form.

 

........................ : .......................

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2b
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One week, the total mass of pears picked was 18 540 kg.
For this week, the ratio mass of apples : mass of pears = 13 : 9.

Find the mass of apples picked that week.

 

............................................... kg

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3
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In a cycling club, the number of members are in the ratio males : females = 8 : 3.
The club has 342 females.

i)

Find the total number of members.

[2]

ii)

Find the percentage of the total number of members that are female.

................................................ % [1]

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4
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One day, the newspaper had 60 pages of news and advertisements.
The ratio  number of pages of news : number of pages of advertisements =  5 colon 7.

i)
Calculate the number of pages of advertisements. 
 
[2]
ii)
Write the number of pages of advertisements as a percentage of the number of pages of news. 
 
........................................... % [1]

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5
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Amol and Priya deliver 645 parcels in the ratio Amol : Priya = 11 : 4.

Calculate the number of parcels Amol delivers.

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6
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Marianne sells photos.
The selling price of each photo is $6.

The selling price for each photo is made up of two parts, printing cost and profit.
For each photo, the ratio       printing cost : profit = 5 : 3.
 

Calculate the profit she makes on each photo.
 

$ ...............................................

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7
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A school has 240 students.
The ratio   girls : boys = 25 : 23.

i)
Show that the number of boys is 115.
 
 

[1]

ii)
One day, there are 15 girls absent and 15 boys absent.
 
Find the ratio   girls : boys in school on this day.
Give your answer in its simplest form.
 
 

..................... : ..................... [2]

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8a
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Adele, Barbara and Collette share $680 in the ratio 9 : 7 : 4.

Show that Adele receives $306.

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8b
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Calculate the amount that Barbara and Collette each receives.

 Barbara $ ...............................................

Collette $ ...............................................

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9
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Here is a list of ingredients to make 20 biscuits.

cie-igcse-2018-may-jun-2-p4-q1a

i)
Find the mass of butter needed to make 35 of these biscuits.


............................................. g [2]

ii)
Michel has 2 kg of each ingredient.

Work out the greatest number of these biscuits that he can make.


[3]

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10
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The Muller family are on holiday in New Zealand.

The family visit two waterfalls, the Humboldt Falls and the Bridal Veil Falls.
The ratio of the heights Humboldt Falls : Bridal Veil Falls = 5 : 1.
The Humboldt Falls are 220 m higher than the Bridal Veil Falls.

Calculate the height of the Humboldt Falls. 

.............................................m

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