Question 1

The angles in a parallelogram are in the ratio $1:3:1:x$.

What is the value of $x$?

Accepted Answer

$x=3$

Answer

$x=-3$

Answer

$x=5$

Answer

$x=1$

Question 2

The angles in a parallelogram are in the ratio $1:3:1:x$. Work out the sizes of all four angles.

Accepted Answer

Angle $1 = 45 \degree$,
Angle $2=135 \degree$,
Angle $3=45 \degree$,
Angle $4=135 \degree$

Answer

Angle $1 = 45 \degree$,
Angle $2=90 \degree$,
Angle $3=60 \degree$,
Angle $4=135 \degree$

Answer

Angle $1 = 90 \degree$,
Angle $2=60 \degree$,
Angle $3=90 \degree$,
Angle $4=60 \degree$

Answer

Angle $1 = 30 \degree$,
Angle $2=45 \degree$,
Angle $3=45 \degree$,
Angle $4=30 \degree$

Question 3

The lengths of the sides of a right-angled triangle are in the ratio $5:12:13$. The shortest side has a length of $	ext {2 cm}.$

Work out the perimeter of the triangle.

Accepted Answer

$	ext {12 cm}$

Answer

$	ext {18 cm}$

Answer

$	ext {26 cm}$

Answer

$	ext {6 cm}$

Question 4

The ratio of pencils to erasers in a school stockroom is $7:2$. There are $90$ more pencils than erasers.

Work out the number of pencils.

Accepted Answer

$126$ pencils

Answer

$102$ pencils

Answer

$98$ pencils

Answer

$84$ pencils

Question 5

The points $A, B, C$ and $D$ form a straight line $ABCD$. 
The ratio of the length of $AB$ to $BC$ is $6:5$.
The ratio of the length of $BC$ to $CD$ is $10:13$.
The total length of $AD$ is $105$cm.
Work out the length of $BC$.

Accepted Answer

$BC=30$cm

Answer

$BC=15$cm

Answer

$BC=25$cm

Answer

$BC=45$cm

Question 6

Kayleigh is two years younger than Hayley.
Bailey is twice as old as Kayleigh.
The sum of their three ages is 38.
Work out the ratio of Bailey’s age to Hayley’s age to Kayleigh’s age.

Accepted Answer

$	ext {B : H : K}$ $= 18:11:9$

Answer

$	ext {B : H : K}$ $= 12:7:11$

Answer

$	ext {B : H : K}$ $= 6:8:5$

Answer

$	ext {B : H : K}$ $= 23:13:8$

Question 7

Carl and Friedrich are playing a trump card game, using all 44 cards from the pack. After a few rounds, Carl is holding 20% more cards than Friedrich.
Work out how many cards they each have.

Accepted Answer

Carl: $24$ cards, Friedrich: $20$ cards

Answer

Carl: $18$ cards, Friedrich: $26$ cards

Answer

Carl: $32$ cards, Friedrich: $12$ cards

Answer

Carl: $30$ cards, Friedrich: $14$ cards

Question 8

The ratio of blue cars to red cars in a traffic survey is $2:1$. In a follow-up survey, the number of blue cars has increased by $50$% and the number of red cars has increased by $25$%.
Work out the new ratio of blue cars to red cars. Give your answer in the form $a:b$, where $a$ and $b$ are integers.

Accepted Answer

$12:5$

Answer

$25:15$

Answer

$5:1$

Answer

$8:3$

Question 9

The ratio of integer $x$ to integer $y$ is $3:2$.
When $x$ is increased by $8$ and $y$ is halved, the ratio becomes $4:1$.
Work out the values of $x$ and $y$.

Accepted Answer

$x=24, y=16$

Answer

$x=14, y=12$

Answer

$x=30, y=19$

Answer

$x=8, y=12$

Question 10

There are some copper coins and silver coins on a table. Each coin is either large or small.
The ratio of copper coins to silver coins is $4:3$.
The ratio of small copper coins to large copper coins is $3:7$.
The ratio of small silver coins to large silver coins is $1:2$.
Work out what fraction of all of the coins are small coins.

Accepted Answer

$\frac{ 11 }{ 35 }$

Answer

$\frac{ 17 }{ 27 }$

Answer

$\frac{ 3 }{ 10 }$

Answer

$\frac{ 1 }{ 5 }$

Question 11

Given that $(2x − 5):6 = 1:(6 − x)$, work out the possible values of $x$.

Accepted Answer

$x = 44.5, x = 4$

Answer

$x = 24, x = 8$

Answer

$x = 48, x = 16$

Answer

$x = 11, x = 3$

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