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Level 1
Level 2
Level 3
Level 4
Level 5
Sharing a quantity in a ratio
26 questions
Lesson
Not started
Mark as done
Share £
40
40
40
in the ratio
3
:
5
3 : 5
3
:
5
.
●
●●●●
Level 1
2 marks
Start
→
Mark as done
Share £
150
150
150
between Jo and Kai in the ratio
2
:
3
2 : 3
2
:
3
.
●●
●●●
Level 2
2 marks
Start
→
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Ali, Bea and Cara share £
4200
4200
4200
in the ratio
2
:
3
:
7
2 : 3 : 7
2
:
3
:
7
Work out how much more Cara receives than Ali. (3 marks)
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●●●
Level 2
3 marks
Start
→
Mark as done
Ann, Ben and Cal share some money in the ratio
2
:
3
:
5
2 : 3 : 5
2
:
3
:
5
Cal receives £
45
45
45
more than Ann.
(a)
Work out the total amount of money shared. [3]
(b)
What fraction of the total does Ben receive? [1]
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●●●
Level 2
4 marks
Start
→
Mark as done
Pink paint is made by mixing red paint and white paint in the ratio
3
:
5
3 : 5
3
:
5
by volume.
Red paint costs £
4
4
4
per litre. White paint costs £
2.50
2.50
2.50
per litre.
Work out the cost of the paint needed to make
2
2
2
litres of pink paint. [3]
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●●●
Level 2
3 marks
Start
→
Mark as done
There are
60
60
60
pens in a pot.
There are only black pens and blue pens in the pot.
number of black pens : number of blue pens
=
1
:
4
= 1 : 4
=
1
:
4
Ravi has to work out how many black pens are in the pot.
He says,
"There are
15
15
15
black pens because
60
÷
4
=
15
60 \div 4 = 15
60
÷
4
=
15
"
Is Ravi correct?
You must give a reason for your answer.
(1 mark)
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●●●
Level 2
1 mark
Start
→
Mark as done
Priya and Quinn share £480 in the ratio 5 : 3. Work out how much more Priya receives than Quinn.
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Level 3
3 marks
Start
→
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In a bag, the ratio of red counters to blue counters is 3 : 5. There are 32 counters in the bag altogether.
(a)
What fraction of the counters are red?
(b)
How many counters are red?
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●●
Level 3
3 marks
Start
→
Mark as done
Two friends share a sum of money in the ratio
3
:
7
3 : 7
3
:
7
.
The
larger
share is £
84
84
84
.
Work out the total amount shared.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The angles of a triangle are in the ratio
2
:
3
:
7
2 : 3 : 7
2
:
3
:
7
.
Work out the size of the
largest
angle.
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Level 3
3 marks
Start
→
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A
B
C
ABC
A
B
C
is a straight line.
A (−3, 5)
B (3, 1)
C
O
x
y
Point
A
A
A
has coordinates
(
−
3
,
5
)
(-3, 5)
(
−
3
,
5
)
Point
B
B
B
has coordinates
(
3
,
1
)
(3, 1)
(
3
,
1
)
B
C
=
3
2
A
B
BC = \frac{3}{2}AB
B
C
=
2
3
A
B
Find the coordinates of point
C
C
C
.
(3 marks)
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Level 3
3 marks
Start
→
Mark as done
Here are two lists of numbers.
List A
18
35
27
40
25
\qquad 18 \qquad 35 \qquad 27 \qquad 40 \qquad 25
18
35
27
40
25
List B
52
x
61
38
\qquad 52 \qquad x \qquad 61 \qquad 38
52
x
61
38
mean of list A : mean of list B
=
2
:
3
= 2 : 3
=
2
:
3
Work out the value of
x
x
x
.
(5 marks)
●●●
●●
Level 3
5 marks
Start
→
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There are only green marbles, blue marbles and white marbles in a tin.
There are
18
18
18
white marbles in the tin.
Priya is going to take at random a marble from the tin.
The probability that the marble will be white is
0.15
0.15
0.15
number of green marbles : number of blue marbles
=
7
:
10
= 7 : 10
=
7
:
10
Work out the number of green marbles in the tin.
(4 marks)
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Level 3
4 marks
Start
→
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A bag of trail mix has a mass of
750
750
750
g.
36
%
36\%
36%
of the mass of the trail mix is raisins and cranberries.
mass of raisins : mass of cranberries
=
5
:
4
= 5 : 4
=
5
:
4
Work out the mass of cranberries in the bag.
(3 marks)
●●●
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Level 3
3 marks
Start
→
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Freya, Tomasz and Ines share some beads in the ratio
3
:
4
:
11
3 : 4 : 11
3
:
4
:
11
Ines gives
3
11
\frac{3}{11}
11
3
of her beads to Freya.
Ines then gives
25
%
25\%
25%
of the rest of her beads to Tomasz.
Ines says,
"We each have the same number of beads now."
Is Ines correct?
You must show how you get your answer.
(4 marks)
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●●
Level 3
4 marks
Start
→
Mark as done
Kwame, Lena and Priya share some marbles in the ratio
3
:
4
:
9
3 : 4 : 9
3
:
4
:
9
Priya gives
1
3
\frac{1}{3}
3
1
of her marbles to Kwame.
Priya then gives
20
%
20\%
20%
of the rest of her marbles to Lena.
Priya says,
"We each have an equal share of the marbles now."
Is Priya correct?
You must show how you get your answer.
(4 marks)
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●●
Level 3
4 marks
Start
→
Mark as done
Two people share an amount of money in the ratio 4 : 7. The smaller share is £96. Work out the total amount of money shared.
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●
Level 4
3 marks
Start
→
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A sum of money is shared between Ali, Beth and Cara in the ratio 2 : 3 : 5. Cara receives £45 more than Ali. Work out the total amount of money shared.
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●
Level 4
4 marks
Start
→
Mark as done
A green paint is made by mixing blue paint and yellow paint in the ratio 2 : 3. Blue paint costs £4.00 per litre and yellow paint costs £3.50 per litre.
Work out the cost of the paint needed to make 20 litres of green paint.
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●
Level 4
4 marks
Start
→
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A prize is shared between three people in the ratio
1
:
4
:
7
1 : 4 : 7
1
:
4
:
7
.
The largest share is £
90
90
90
more than the smallest share.
Work out the total prize.
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●
Level 4
3 marks
Start
→
Mark as done
Trail mix is made from nuts and raisins in the ratio
3
:
2
3 : 2
3
:
2
by weight
.
Nuts cost £
6
6
6
per kg. Raisins cost £
3
3
3
per kg.
Work out the cost of the ingredients for
4
4
4
kg of trail mix.
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●
Level 4
4 marks
Start
→
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6
6
6
m of green ribbon and
4
4
4
m of gold ribbon cost a total of
680
680
680
p
cost of
1
1
1
m of green ribbon : cost of
1
1
1
m of gold ribbon
=
3
:
4
= 3 : 4
=
3
:
4
Work out the cost of
1
1
1
m of green ribbon and the cost of
1
1
1
m of gold ribbon.
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
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There are only lemon cupcakes and chocolate cupcakes on tray A.
number of lemon cupcakes : number of chocolate cupcakes
=
2
:
7
= 2 : 7
=
2
:
7
Tray B holds only vanilla cupcakes and coffee cupcakes.
Tray B holds a third as many cupcakes as tray A.
There are
x
x
x
lemon cupcakes on tray A.
Use algebra to show that, altogether, trays A and B hold
6
x
6x
6
x
cupcakes.
(3 marks)
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●
Level 4
3 marks
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→
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F
G
H
FGH
F
G
H
and
J
F
G
JFG
J
F
G
are similar isosceles triangles.
F
G
H
J
F
G
=
F
H
FG = FH
F
G
=
F
H
J
F
=
J
G
JF = JG
J
F
=
J
G
G
H
J
GHJ
G
H
J
is a straight line.
G
H
:
H
J
=
9
:
7
GH : HJ = 9 : 7
G
H
:
H
J
=
9
:
7
Find the ratio
F
G
:
F
J
FG : FJ
F
G
:
F
J
(3 marks)
●●●●●
Level 5
3 marks
Start
→
Mark as done
A
B
D
L
O
x
y
In the diagram
A
A
A
is the point
(
0
,
10
)
(0, 10)
(
0
,
10
)
B
B
B
is the point
(
15
,
0
)
(15, 0)
(
15
,
0
)
D
D
D
is the point on
A
B
AB
A
B
such that
A
D
:
D
B
=
2
:
3
AD : DB = 2 : 3
A
D
:
D
B
=
2
:
3
The line
L
L
L
passes through
D
D
D
.
The gradient of
L
L
L
is
2.5
2.5
2.5
L
L
L
passes through the point with coordinates
(
−
3
,
f
)
(-3, f)
(
−
3
,
f
)
Show that
f
<
−
16
f < -16
f
<
−
16
(5 marks)
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Level 5
5 marks
Start
→
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A box holds
y
y
y
counters:
x
x
x
are red,
3
3
3
are white and the others are yellow.
x
:
y
=
1
:
4
x : y = 1 : 4
x
:
y
=
1
:
4
Seb takes at random two counters from the box.
Find an expression, in terms of
x
x
x
, for the probability that both counters are the same colour.
Give your answer as a fraction in the form
a
x
2
+
b
x
+
c
d
x
2
+
e
x
\dfrac{ax^2 + bx + c}{dx^2 + ex}
d
x
2
+
e
x
a
x
2
+
b
x
+
c
where
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
and
e
e
e
are integers.
(5 marks)
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Level 5
5 marks
Start
→
Ratio problems where the amounts change
18 questions
Lesson
Not started
Mark as done
Simplify the ratio
12
:
18
12 : 18
12
:
18
.
●
●●●●
Level 1
1 mark
Start
→
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Write the ratio
50
50
50
p to £
2
2
2
in its simplest form.
●
●●●●
Level 1
2 marks
Start
→
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In a class the ratio of boys to girls is
2
:
3
2 : 3
2
:
3
. There are
12
12
12
boys. How many girls are there?
●
●●●●
Level 1
2 marks
Start
→
Mark as done
Orange squash is made by mixing squash and water in the ratio
1
:
4
1 : 4
1
:
4
. How much water is needed for
200
200
200
ml of squash?
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Write the ratio
3
:
12
3 : 12
3
:
12
in the form
1
:
n
1 : n
1
:
n
.
●
●●●●
Level 1
1 mark
Start
→
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A recipe for
4
4
4
people uses
300
300
300
g of flour. How much flour is needed for
6
6
6
people?
●●
●●●
Level 2
2 marks
Start
→
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A bag contains red and blue marbles in the ratio
3
:
7
3 : 7
3
:
7
There are
40
40
40
marbles in the bag.
(a)
How many more blue marbles than red marbles are there? (2 marks)
5
5
5
more red marbles are added to the bag.
(b)
Write the new ratio of red to blue marbles in its simplest form. (1 mark)
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●●●
Level 2
3 marks
Start
→
Mark as done
The ratio of adults to children at a swimming pool was
3
:
5
3 : 5
3
:
5
Then
18
18
18
more adults arrived. No one left.
The ratio of adults to children became
3
:
4
3 : 4
3
:
4
Work out how many children were at the pool. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
In a car park, the ratio of cars to vans is 7 : 2. There are 45 more cars than vans. Work out the total number of vehicles in the car park.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A recipe for 4 people uses flour and sugar in the ratio 5 : 2. The recipe for 4 people needs 350 g of flour. Work out how much sugar is needed to make the recipe for 6 people.
●●●●
●
Level 4
4 marks
Start
→
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At a show, the ratio of the number of adults to the number of children is 4 : 5. There are 216 people at the show in total. Then 40 more adults arrive. Work out the new ratio of adults to children. Give your answer in its simplest form.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
At a shelter, the ratio of dogs to cats is
9
:
4
9 : 4
9
:
4
.
There are
35
35
35
more dogs than cats.
Work out the total number of animals.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A recipe for
6
6
6
people uses butter and flour in the ratio
3
:
8
3 : 8
3
:
8
.
The recipe for
6
6
6
people needs
320
320
320
g of flour.
Work out how much
butter
is needed for
9
9
9
people.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A choir has
88
88
88
members. The ratio of boys to girls is
5
:
6
5 : 6
5
:
6
.
Then
4
4
4
boys join the choir and
8
8
8
girls leave.
Work out the new ratio of boys to girls, in its simplest form.
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●
Level 4
3 marks
Start
→
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In a box, the ratio of red beads to blue beads is 3 : 4. When 6 more red beads are added to the box, the ratio of red beads to blue beads becomes 9 : 8. Work out the original number of blue beads.
●●●●●
Level 5
4 marks
Start
→
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Jar A and Jar B contain marbles in the ratio 5 : 3. When 8 marbles are moved from Jar A to Jar B, the two jars then contain marbles in the ratio 1 : 1. Work out how many marbles were in Jar A to begin with.
●●●●●
Level 5
4 marks
Start
→
Mark as done
In a drawer, the ratio of pens to pencils is
2
:
5
2 : 5
2
:
5
.
When
9
9
9
more pens are put in the drawer, the numbers of pens and pencils become
equal
.
Work out the total number of items in the drawer
after
the pens are added.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Two boxes,
A
A
A
and
B
B
B
, contain counters in the ratio
7
:
3
7 : 3
7
:
3
.
When
12
12
12
counters are moved from box
A
A
A
to box
B
B
B
, the two boxes contain
equal
numbers.
Work out the total number of counters.
●●●●●
Level 5
3 marks
Start
→
Combining and relating ratios
21 questions
Lesson
Not started
Mark as done
a
:
b
=
2
:
3
a : b = 2 : 3
a
:
b
=
2
:
3
and
b
:
c
=
3
:
5
b : c = 3 : 5
b
:
c
=
3
:
5
. Write
a
:
b
:
c
a : b : c
a
:
b
:
c
.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
p
:
q
=
3
:
4
p : q = 3 : 4
p
:
q
=
3
:
4
. Write
p
p
p
as a fraction of the total of
p
p
p
and
q
q
q
.
●
●●●●
Level 1
1 mark
Start
→
Mark as done
x
:
y
=
1
:
2
x : y = 1 : 2
x
:
y
=
1
:
2
and
y
:
z
=
4
:
3
y : z = 4 : 3
y
:
z
=
4
:
3
. Write
x
:
y
:
z
x : y : z
x
:
y
:
z
in its simplest form.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
In a bag, red : blue counters
=
3
:
1
= 3 : 1
=
3
:
1
and blue : green
=
2
:
5
= 2 : 5
=
2
:
5
. Write red : blue : green.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
a
:
b
=
5
:
2
a : b = 5 : 2
a
:
b
=
5
:
2
and
b
:
c
=
2
:
7
b : c = 2 : 7
b
:
c
=
2
:
7
. Given that
b
=
6
b = 6
b
=
6
, find
a
a
a
and
c
c
c
.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
m
:
n
=
1
:
3
m : n = 1 : 3
m
:
n
=
1
:
3
and
n
:
k
=
6
:
1
n : k = 6 : 1
n
:
k
=
6
:
1
. Write
m
:
n
:
k
m : n : k
m
:
n
:
k
.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
a
:
b
=
2
:
3
a : b = 2 : 3
a
:
b
=
2
:
3
and
b
:
c
=
4
:
5
b : c = 4 : 5
b
:
c
=
4
:
5
Work out
a
:
b
:
c
a : b : c
a
:
b
:
c
(2 marks)
●●
●●●
Level 2
2 marks
Start
→
Mark as done
There are
252
252
252
tiles in a box.
There are only white tiles, grey tiles and black tiles.
2
9
\frac{2}{9}
9
2
of the
252
252
252
tiles are white tiles.
number of grey tiles : number of black tiles
=
2
:
5
= 2 : 5
=
2
:
5
number of black tiles : number of white tiles
=
n
:
1
= n : 1
=
n
:
1
(a)
Work out the value of
n
n
n
.
You must show all your working.
(5 marks)
6
6
6
of the grey tiles are cracked and are taken out of the box.
(b)
Does this affect your answer to part (a)?
Give a reason for your answer.
(1 mark)
●●●
●●
Level 3
6 marks
Start
→
Mark as done
Dev has some small, medium and large candles.
He has a total of
500
500
500
candles.
3
5
\frac{3}{5}
5
3
of the
500
500
500
candles are scented.
For the scented candles,
number of small candles : number of medium candles
=
1
:
3
= 1 : 3
=
1
:
3
number of medium candles : number of large candles
=
6
:
7
= 6 : 7
=
6
:
7
Work out the percentage of Dev's candles that are small scented candles.
(5 marks)
●●●
●●
Level 3
5 marks
Start
→
Mark as done
a
:
b
=
3
:
4
a : b = 3 : 4
a
:
b
=
3
:
4
and
b
:
c
=
6
:
5
b : c = 6 : 5
b
:
c
=
6
:
5
. Work out
a
:
b
:
c
a : b : c
a
:
b
:
c
, giving your answer in its simplest form.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In a school orchestra, the ratio of violin players to flute players is
5
:
3
5 : 3
5
:
3
.
The ratio of flute players to cello players is
2
:
1
2 : 1
2
:
1
.
(a)
Find the ratio of violin players to flute players to cello players. Give your answer in its simplest form.
(b)
There are 38 players in the orchestra altogether.
Work out how many cello players there are.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
On a map, a length of 4 cm represents an actual distance of 10 km. Write the scale of the map as a ratio in the form 1 : n.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
a
:
b
=
2
:
3
a : b = 2 : 3
a
:
b
=
2
:
3
and
b
:
c
=
4
:
7
b : c = 4 : 7
b
:
c
=
4
:
7
Work out
a
:
b
:
c
a : b : c
a
:
b
:
c
, giving your answer in its simplest form.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In a fruit box, the ratio of apples to bananas is
5
:
2
5 : 2
5
:
2
, and the ratio of bananas to cherries is
3
:
4
3 : 4
3
:
4
.
(a)
Work out the ratio apples : bananas : cherries in its simplest form.
The box contains
40
40
40
cherries.
(b)
How many apples does it contain?
●●●●
●
Level 4
4 marks
Start
→
Mark as done
On a map, a length of
4
4
4
cm represents an actual distance of
6
6
6
km.
Write the scale of the map as a ratio in the form
1
:
n
1 : n
1
:
n
●●●●
●
Level 4
3 marks
Start
→
Mark as done
In a company, the ratio of managers to staff is 1 : 8, and the ratio of staff to trainees is 4 : 3. There are 96 staff. Work out the total number of managers, staff and trainees in the company.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The ratio
(
2
x
+
1
)
:
(
x
+
4
)
(2x + 1) : (x + 4)
(
2
x
+
1
)
:
(
x
+
4
)
is equal to the ratio
3
:
2
3 : 2
3
:
2
. Work out the value of
x
x
x
.
●●●●●
Level 5
3 marks
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→
Mark as done
The ratio
(
3
x
−
2
)
:
(
x
+
6
)
(3x - 2) : (x + 6)
(
3
x
−
2
)
:
(
x
+
6
)
is equal to the ratio
5
:
3
5 : 3
5
:
3
Work out the value of
x
x
x
.
●●●●●
Level 5
3 marks
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→
Mark as done
p
:
q
=
2
:
5
p : q = 2 : 5
p
:
q
=
2
:
5
and
q
:
r
=
10
:
7
q : r = 10 : 7
q
:
r
=
10
:
7
r
r
r
is
12
12
12
more than
p
p
p
.
Work out the value of
q
q
q
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows three triangles,
O
A
B
OAB
O
A
B
,
O
C
D
OCD
O
C
D
and
O
E
F
OEF
O
E
F
.
O
A
C
E
B
D
F
O
A
C
E
OACE
O
A
C
E
and
O
B
D
F
OBDF
O
B
D
F
are straight lines.
A
B
AB
A
B
,
C
D
CD
C
D
and
E
F
EF
E
F
are parallel.
O
A
:
A
C
:
C
E
=
2
:
3
:
4
OA : AC : CE = 2 : 3 : 4
O
A
:
A
C
:
C
E
=
2
:
3
:
4
Show that
area of triangle
O
A
B
OAB
O
A
B
: area of
A
B
D
C
ABDC
A
B
D
C
: area of
C
D
F
E
CDFE
C
D
F
E
=
4
:
21
:
56
= 4 : 21 : 56
=
4
:
21
:
56
(3 marks)
●●●●●
Level 5
3 marks
Start
→
Mark as done
3
a
:
2
c
=
4
:
5
3a : 2c = 4 : 5
3
a
:
2
c
=
4
:
5
b
:
4
c
=
3
:
2
b : 4c = 3 : 2
b
:
4
c
=
3
:
2
Show that
a
+
b
:
b
+
c
=
14
:
15
a + b : b + c = 14 : 15
a
+
b
:
b
+
c
=
14
:
15
(3 marks)
●●●●●
Level 5
3 marks
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→