WJEC GCSE Maths
Topic questions Ratio, proportion and rates of change Ratio
38 questions · 173 marks · about 4 hours
A mass is shared in the ratio 3: 5.
The larger share is 44 lb (pounds).
Calculate the total mass.
Give your answer in kilograms (kg).
You must show all your working.
Calculate the value of the smaller share.
You must show all your working.
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
A mass is shared in the ratio 3: 5. The larger share is 44 lb (pounds).
Calculate the total mass.
Give your answer in kilograms (kg).
You must show all your working.
Calculate the value of the smaller share.
You must show all your working.
A money box contains some 20p coins and some 50p coins.
The value of the 20p coins is £19.20.
The ratio of the number of 20p coins to the number of 50p coins is 8: 5.
Find the total value of the coins in the money box.
You must show all your working.
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
A money box contains some 20p coins and some 50p coins. The value of the 20p coins is £19.20.
The ratio of the number of 20p coins to the number of 50p coins is 8: 5.
Find the total value of the coins in the money box.
You must show all your working.
Express 96 as a percentage of 300.
Share £48 in the ratio 1: 7.
Express 96 as a percentage of 300.
Share £48 in the ratio 1: 7.
Aled and Berwyn share £ x in the ratio 2: 3.
Aled’s share of the money is £0.4x.
What is Berwyn’s share of the money in terms of x?
Carys and Delyth share the same amount, £x, in the ratio 3: 7.
Show that one of these four people receives the same amount as the combined total of
two of the other people.
Aled and Berwyn share £ x in the ratio 2: 3.
Aled’s share of the money is £0.4x.
What is Berwyn’s share of the money in terms of x?
Carys and Delyth share the same amount, £x, in the ratio 3: 7.
Show that one of these four people receives the same amount as the combined total of
two of the other people.
There are many socks in a drawer.
The socks are red, green, blue or pink.
A sock is chosen at random from the drawer.
Complete the table below.
| Colour | Red | Green | Blue | Pink |
| Probability | 0·3 | 0·1 | 0·25 |
In the drawer, there are 20 pink socks.
How many red socks are there in the drawer?
The shape below has a total length of 35 cm. The shape is cut into three parts, A, B and C.
The length of A is 
of the total length of the shape. The lengths of B and C are in the ratio 1: 6.
Find the length of each part of the shape.
You must show all your working.
Kamal worked for a total of 36 hours in one week.
On Monday, Tuesday and Wednesday, he worked the same number of hours each day. On both Thursday and Friday, he worked for half as long as he did on any of the first three days. He did not work on Saturday or Sunday.
How many hours did Kamal work for on Friday?
Kamal worked for…………........ …………………. hours on Friday
Express 48 as a percentage of 400.
Share £45 in the ratio 8: 1.
£........ and £........
Express 1
as a single fraction in the form 
, where a and b are integers.
Express 48 as a percentage of 400.
Share £45 in the ratio 8: 1.
£........ and £........
Express 1 as a single fraction in the form , where a and b are integers.
A large number of prize tokens are placed in a box.
The tokens are identical in shape and size.
Gold, Silver, Bronze or No Prize is written on each token.
One token is chosen at random from the box. The table below shows the probability of choosing a Gold prize token and the probability of choosing a Silver prize token.
| Token | Gold | Silver | Bronze | No Prize |
| Probability | 0·02 | 0·18 |
There are three times as many No Prize tokens in the box as there are Bronze prize tokens.
Complete the table.
There are 15 Gold prize tokens in the box.
How many Silver prize tokens are there in the box?
A sphere has a diameter of 6 cm.
A cone has a base radius of 10 cm and a height of 9 cm.
Find the ratio of the volume of the sphere to the volume of the cone.
Give your answer in its simplest form.
Volume of the sphere: Volume of the cone
A large number of prize tokens are placed in a box.
The tokens are identical in shape and size.
Gold, Silver, Bronze or No Prize is written on each token.
One token is chosen at random from the box. The table below shows the probability of choosing a Gold prize token and the probability of choosing a Silver prize token.
| Token | Gold | Silver | Bronze | No Prize |
| Probability | 0·02 | 0·18 |
There are three times as many No Prize tokens in the box as there are Bronze prize tokens.
Complete the table.
There are 15 Gold prize tokens in the box.
How many Silver prize tokens are there in the box?
A sum of money is shared in the ratio 1: 8.
The larger share is £16.80. What is the total amount of money shared?
You must show all your working.
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
A sum of money is shared in the ratio 1: 8. The larger share is £16.80. What is the total amount of money shared?
You must show all your working.
The height of a cylinder is 24·8 cm. The ratio of the diameter of the cylinder to the height of the cylinder is 3: 2.
Find the volume of the cylinder. Give your answer correct to 2 significant figures.
You must show all your working.
The height of a cylinder is 24·8 cm. The ratio of the diameter of the cylinder to the height of the cylinder is 3: 2.
Find the volume of the cylinder. Give your answer correct to 2 significant figures.
You must show all your working.
The sizes of angles a and b in the triangle shown below are in the ratio 2: 3.
Diagram not drawn to scale
Calculate the size of each of the angles a and b.
You must show all your working.
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The sizes of angles a and b in the triangle shown below are in the ratio 2: 3.
Diagram not drawn to scale
Calculate the size of each of the angles a and b. You must show all your working. [3 + 2 OCW]
A sum of money is shared in the ratio 3: 4: 7.
The smallest share is £210. What is the total amount of money shared?
You must show all your working.
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
A sum of money is shared in the ratio 3: 4: 7. The smallest share is £210.
What is the total amount of money shared?
You must show all your working.
18% of £256 is shared in the ratio 2: 1. Calculate the value of the larger share. Give your answer to the nearest 10p.
You must show all your working.
In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
18% of £256 is shared in the ratio 2: 1. Calculate the value of the larger share. Give your answer to the nearest 10p.
You must show all your working.
Share £720 in the ratio 2: 7.
Calculate the value of the reciprocal of 0.2. (b)
Calculate the value of the reciprocal of 0.2. 
(b)
A box contains many discs, identical in shape and size.
A picture of one of four Welsh castles is printed on each disc.
A disc is chosen at random from the box. Complete the table below to find the probability of choosing a disc showing Dinefwr
In the box, there were 522 discs showing a picture of Caernarfon Castle.
How many of the discs showed a picture of Harlech Castle?
A box contains many discs, identical in shape and size.
A picture of one of four Welsh castles is printed on each disc.
A disc is chosen at random from the box. Complete the table below to find the probability of choosing a disc showing Dinefwr
In the box, there were 522 discs showing a picture of Caernarfon Castle.
How many of the discs showed a picture of Harlech Castle?
Also involves Simplifying and manipulating expressions
A cylinder just fits inside a hollow cube with sides of length m cm.
The radius of the cylinder is 
cm. The height of the cylinder is mcm.
The ratio of the volume of the cube to the volume of the cylinder is given by
volume of cube: volume of cylinder
= k: 
,
where k is a number.
Find the value of k.
You must show all your working.
Express 54 as a percentage of 129.
Give your answer to the nearest whole number.
Share 25·8 kg in the ratio 5: 1.
Also involves Simplifying and manipulating expressions
A cylinder just fits inside a hollow cube with sides of length m cm.
The radius of the cylinder is cm. The height of the cylinder is mcm.
The ratio of the volume of the cube to the volume of the cylinder is given by
volume of cube: volume of cylinder
= k: ,
where k is a number.
Find the value of k.
You must show all your working.
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