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Level 5
Sharing a quantity in a ratio
26 questions
Lesson
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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
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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
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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.
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Level 3
3 marks
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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
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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
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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)
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Level 3
5 marks
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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
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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
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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
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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
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Ratio problems where the amounts change
18 questions
Lesson
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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)
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Level 3
3 marks
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Combining and relating ratios
21 questions
Lesson
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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)
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Level 3
6 marks
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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)
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Level 3
5 marks
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