1
1 Alex, Bobbie and Chris share strawberries in the ratio Alex : Bobbie : Chris = 3 : 2 : 2.
Chris receives 12 strawberries.
Calculate the total number of strawberries shared.
................................................... [2]
[Total: 2]
2 Of the 852 workers in a company, the ratio part-time workers : full-time workers = 5 : 7.
Calculate the number of full-time workers.
................................................... [2]
[Total: 2]
3
Painter Plumber Electrician
$48 per hour
$35 per hour Fixed charge $40
for the first 2 hours
plus then
$26.50 per hour $32 per hour
These are the rates charged by a painter, a plumber and an electrician who do some work for Mr Sharma.
(a) The painter works for 7 hours.
Calculate the amount Mr Sharma pays the painter.
$ ................................................... [1]
2
(b) Mr Sharma pays the plumber $252.
Calculate how many hours the plumber works.
................................................... hours [2]
(c) Mr Sharma pays the electrician $224.
Calculate how many hours the electrician works.
................................................... hours [2]
(d) Write down the ratio of the amount Mr Sharma pays to the painter, the plumber and the electrician.
Give your answer in its lowest terms.
painter : plumber : electrician = .............................. : .............................. : .............................. [2]
[Total: 7]
3
4 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.
$ ................................................... [4]
[Total: 4]
5 The visitors to a campsite today are in the ratio
men : women = 5 : 4 and women : children = 3 : 7.
(a) Calculate the ratio men : women : children in its simplest form.
.................... : .................... : .................... [2]
(b) Today there are 224 children at the campsite.
Calculate the total number of men and women.
................................................... [3]
[Total: 5]
4
6 Divide $24 in the ratio 7 : 5.
$ .............................. , $ .............................. [2]
[Total: 2]
7 One day, a newspaper had 60 pages of news and advertisements.
The ratio number of pages of news : number of pages of advertisements = 5 : 7.
(a) Calculate the number of pages of advertisements.
................................................... [2]
(b) Write the number of pages of advertisements as a percentage of the number of pages of news.
................................................... % [1]
[Total: 3]
8 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
(a) For the standard fare, write the ratio adult fare : child fare in its simplest form.
.............................. : .............................. [1]
(b) For an adult, find the percentage increase in the cost of the standard fare to the premier fare.
................................................... % [3]
5
(c) 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.
$ ................................................... [5]
[Total: 9]
9 Amol and Priya deliver 645 parcels in the ratio Amol : Priya = 11 : 4.
Calculate the number of parcels Amol delivers.
................................................... [2]
[Total: 2]
10 Marianne sells photos.
The selling price of each photo is $6.
6
(a) 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.
$ ................................................... [2]
(b) Calculate her profit as a percentage of the selling price.
................................................... % [1]
(c) Calculate the selling price of a photo in euros (€) when the exchange rate is €1 = $1.091 .
€ ................................................... [2]
[Total: 5]
11 A 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 [2]
[Total: 2]
7
12 A school has 240 students.
The ratio girls : boys = 25 : 23.
(a) Show that the number of boys is 115.
[1]
(b) 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]
[Total: 3]
13 Here is a list of ingredients to make 20 biscuits.
(a) Find the mass of rice as a percentage of the mass of sugar.
................................................... % [1]
(b) Find the mass of butter needed to make 35 of these biscuits.
................................................... g [2]
8
(c) Michel has 2 kg of each ingredient.
Work out the greatest number of these biscuits that he can make.
................................................... [3]
[Total: 6]
14 The 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.
(a) Find the ratio of the number in group A to the number in group C.
Give your answer in its simplest form.
.............................. : .............................. [3]
9
(b) There are 45 people in group C.
Find the total number of people who work for the company.
................................................... [3]
[Total: 6]
15 A car of length 4.3 m is travelling at 105 km/h.
It passes over a bridge of length 36 m.
Calculate the time, in seconds, it takes to pass over the bridge completely.
................................................... s [3]
[Total: 3]
16 Pip and Ali share $785 in the ratio Pip : Ali = 4 : 1.
Work out Pip’s share.
Answer $ ................................................... [2]
[Total: 2]
10
17 The scale on a map is 1 : 50 000.
The area of a field on the map is 1.2 square centimetres.
Calculate the actual area of the field in square kilometres.
Answer ................................................... km2 [2]
[Total: 2]
18 Tins of paint are filled at the rate of 2 m3 per minute.
How many 750 ml tins of paint can be filled in 1 hour?
Answer ................................................... [3]
[Total: 3]
19 A train passes through a station at a speed of 108 km/h.
The length of the station is 120 m.
The train takes 7 seconds to completely pass through the station.
Work out the length of the train.
................................................... m [3]
[Total: 3]
11
20 A train of length 105 m takes 11 seconds to pass completely through a station of length 225 m.
Calculate the speed of the train in km/h.
................................................... km/h [3]
[Total: 3]
21 A train journey takes 5 hours 54 minutes.
The average speed of the train for this journey is 80 km/h.
Calculate the distance travelled.
................................................... km [2]
[Total: 2]
22 The distance between Prague and Vienna is 254 kilometres.
The local time in Prague is the same as the local time in Vienna.
A train leaves Prague at 15 20 and arrives in Vienna at 19 50 the same day.
Calculate the average speed of the train.
................................................... km/h [2]
[Total: 2]
23 Here is part of a train timetable for a journey from London to Marseille.
All times given are in local time.
The local time in Marseille is 1 hour ahead of the local time in London.
12
London 07 19
Ashford 07 55
Lyon 13 00
Avignon 14 08
Marseille 14 16
(a) Work out the total journey time from London to Marseille.
Give your answer in hours and minutes.
.............................. h .............................. min [2]
(b) The distance from London to Ashford is 90 km.
The local time in London is the same as the local time in Ashford.
Work out the average speed, in km/h, of the train between London and Ashford.
................................................... km/h [3]
[Total: 5]
24 A train takes 35 seconds to completely cross a bridge.
The average speed of the train during this crossing is 90 km/h.
The length of the train is 95 metres.
Calculate the length, in metres, of this bridge.
................................................... m [4]
13
[Total: 4]
25 Priya drives her van a distance of 54 km.
She leaves at 10 55 and arrives at 12 38.
Calculate her average speed.
................................................... km/h [3]
[Total: 3]
26 Amol drives his truck at an average speed of 50 km/h.
He leaves at 07 00 and arrives at 11 15.
Calculate the distance he drives.
................................................... km [2]
[Total: 2]
27 A car travels at 56 km/h.
Find the time it takes to travel 300 metres.
Give your answer in seconds correct to the nearest second.
Answer ................................................... s [4]
[Total: 4]
14
28
45
NOT TO
SCALE
Speed
(km/h)
0
10 20 30
Time (seconds)
The diagram shows the speed-time graph of a car.
The car travels at 45 km/h for 20 seconds.
The car then decelerates for 10 seconds until it stops.
(a) Change 45 km/h into m/s.
Answer(a) ................................................... m/s [2]
(b) Find the deceleration of the car, giving your answer in m/s2.
Answer(b) ................................................... m/s2 [1]
(c) Find the distance travelled by the car during the 30 seconds, giving your answer in metres.
Answer(c) ................................................... m [3]
[Total: 6]
15
29 A car travels a distance of 1280 metres at an average speed of 64 kilometres per hour.
Calculate the time it takes for the car to travel this distance.
Give your answer in seconds.
Answer ................................................... s [3]
[Total: 3]
30
William Toby
Town 4
Distance
2
(km)
Home 0
10 00 10 04 10 08 10 12 10 16 10 20 10 24 10 28 10 32
Time
Toby and William cycled into town.
Their journeys are shown on the travel graph.
(a) For how many minutes did Toby stop on his journey into town?
Answer(a) ................................................... min [1]
16
(b) Explain what happened at 10 20.
Answer(b)......................................................................................................................................... [1]
(c) Work out how long William took to cycle into town.
Answer(c) ................................................... min [1]
(d) Calculate William’s speed in km/h.
Answer(d) ................................................... km/h [2]
[Total: 5]
31 A shop sells three different sized boxes of rice.
The boxes all have the same cost per kilogram.
NOT TO
SCALE
Box A Box B Box C
80 rupees $3.50
750 g 1.35 kg
(a) Work out the cost in rupees of box B.
................................................... rupees [2]
17
(b) $1 = 64 rupees.
Calculate the mass of box C.
Give your answer in kilograms.
................................................... kg [3]
[Total: 5]
32 Parthi advertises a frame for a price of $57 or 48.20 euros.
The exchange rate is $1= 0.88 euros.
Calculate the difference between these prices, in dollars and cents, correct to the nearest cent.
$ ................................................... [3]
[Total: 3]
33 Raj buys some sand for 3540 rupees.
Calculate the cost in dollars when the exchange rate is $1 = 70.8 rupees.
$ ................................................... [2]
[Total: 2]
34 For a concert in a theatre, the ticket prices are in the ratio
Section A : Section B : Section C = 9 : 7 : 4.
A ticket for Section C costs $6.
18
(a) Show that a ticket for Section B costs $10.50 .
[1]
(b) Find the cost of a ticket for Section A.
$ ................................................... [1]
(c) The table shows the number of tickets sold in each section.
Section Number of tickets sold
A 120
B 136
C 30
Calculate the total amount received from the ticket sales.
$ ................................................... [3]
(d) The concert costs $4500 to organise.
Calculate the amount received from the ticket sales as a percentage of the $4500.
................................................... % [1]
[Total: 6]
19
35
Campsite fees
(per day)
Tent ............. $15.00
Caravan ....... $25.00
The sign shows the fees charged at a campsite.
Today there are 54 tents and 18 caravans on the site.
Calculate the fees charged today.
$ ................................................... [2]
[Total: 2]
36 Here is part of the menu for Jamie’s café.
Menu
Price ($)
Tea 2.35
Coffee 3.40
Lemonade 1.80
Cake 4.45
Biscuit 0.85
(a) Sue has one tea and one cake.
Calculate how much she pays.
$ ................................................... [1]
20
(b) Derrick has one coffee and two biscuits.
How much change does he receive from a $10 note?
$ ................................................... [2]
[Total: 3]
37 On holiday Maria paid 2.25 euros for the newspaper when the exchange rate was $1 = 0.9416 euros.
At home Maria paid $1.13 for the newspaper.
Calculate the difference in price.
Give your answer in dollars, correct to the nearest cent.
$ ................................................... [3]
[Total: 3]
38 The Muller family are on holiday in New Zealand.
(a) They change some euros (€) and receive $1962 (New Zealand dollars).
The exchange rate is €1 = $1.635 .
Calculate the number of euros they change.
€ ................................................... [2]
21
(b) The family spend 15% of their New Zealand dollars on a tour.
Calculate the number of dollars they have left.
$ ................................................... [2]
[Total: 4]
39 Adele changes $306 into euros (€) when the exchange rate is €1 = $1.125 .
Calculate the number of euros she receives.
€ ................................................... [2]
[Total: 2]
40 A shop sells dress fabric for $2.97 per metre.
(a) A customer buys 9 metres of this fabric.
Calculate the change he receives from $50.
$ ................................................... [2]
22
(b) The selling price of $2.97 per metre is an increase of 8% on the cost price.
Calculate the cost price.
$ ................................................... per metre [3]
[Total: 5]
