Ratio - Worksheets, Questions and Revision

20 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Ratio, Proportion and Rates of Change

3.5 Ratio

EDEXCEL 1MA1 · Calculator allowed · about 70 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Revision notes: Ratio

Sharing an amount in a given ratio splits a total quantity into parts according to a ratio, such as sharing 60 pounds in the ratio 2:3. Ratio problems can also work in the other direction, using one known share to find the total or another share.

Add up all the parts of the ratio to find the TOTAL number of parts.
Divide the total amount by the total number of parts to find the value of ONE part.
Multiply the value of one part by each number in the ratio to find each share.
For 'given one share, find the total' problems, first find the value of one part from the known share, then multiply by the total number of parts (or by any other part needed).

Worked example. Share 84 pounds between Alex and Ben in the ratio 3:4.

Total number of parts = 3 + 4 = 7.
Value of one part = 84 / 7 = 12 pounds.
Alex's share = 3 x 12 = 36 pounds.
Ben's share = 4 x 12 = 48 pounds.
Check: 36 + 48 = 84, which matches the total.

Answer: Alex gets 36 pounds; Ben gets 48 pounds.

Zara and Amir share 20 sweets in the ratio 1:4.

(Total for Question 1 is 2 marks)

A total of 60 is shared between three people in the ratio 1:2:3. Which of these is the largest share?

A) 10
B) 20
C) 30
D) 40

(Total for Question 2 is 1 mark)

Kwame and Dev share 45 kg of compost in the ratio 4:5. Work out how much compost Kwame receives.

(Total for Question 3 is 2 marks)

Ayesha and Ben share 360 pounds in the ratio 4:5. Work out how much money Ben receives.

(Total for Question 4 is 3 marks)

A necklace is made using red, blue and green beads in the ratio 2:3:5. There are 60 beads in total.

(a)Work out the number of green beads.(3)

(b)Work out the number of red and blue beads combined.(2)

(Total for Question 5 is 5 marks)

The ratio of cats to dogs at a rescue centre is 3:7. There are 21 cats at the centre.

(a)Work out the number of dogs at the centre.(2)

(b)Work out the total number of animals at the centre.(1)

(Total for Question 6 is 3 marks)

A prize fund of 200 pounds is shared between three charities in the ratio 2:3:5.

(a)Work out what fraction of the fund the charity with the largest share receives.(2)

(b)Work out how much money that charity receives.(2)

(Total for Question 7 is 4 marks)

Chloe, Mo and Nia are business partners. They share a profit of 960 pounds in the ratio 2:3:7. Work out how much profit each partner receives.

(Total for Question 8 is 3 marks)

Aaliyah has a photograph that is 15 cm wide. She enlarges the photograph in the ratio 3:5. Work out the width of the enlarged photograph.

(Total for Question 9 is 3 marks)

A cleaning solution is made by mixing disinfectant and water in the ratio 1:9. Bilal has 2.5 litres of disinfectant and wants to use all of it, keeping the same ratio. Work out the total volume of solution he can make.

(Total for Question 10 is 3 marks)

A shop sells oats in two sizes.
Small bag: 500 g for 1.20 pounds.
Large bag: 1.4 kg for 3.15 pounds.
Determine which bag is the better value for money.

(Total for Question 11 is 3 marks)

A football squad has 24 players. The ratio of forwards to midfielders to defenders is 3:5:4. Work out the percentage of the squad who are defenders.

(Total for Question 12 is 3 marks)

Given that 5:x = 15:24, work out the value of x.

(Total for Question 13 is 2 marks)

Ravi and Nia share 150 pounds in the ratio 2:3. Work out how much more money Nia receives than Ravi.

(Total for Question 14 is 3 marks)

In a box of pens, the ratio of blue pens to black pens is 5:3. There are 12 more blue pens than black pens. Work out the total number of pens in the box.

(Total for Question 15 is 3 marks)

Grey paint is made by mixing blue paint and white paint in the ratio 3:2. Yusuf wants to make 40 litres of grey paint using this ratio. Work out how many litres of blue paint and how many litres of white paint he needs.

(Total for Question 16 is 3 marks)

In a survey, the ratio of people who prefer tea to coffee is 5:4. The ratio of people who prefer coffee to hot chocolate is 3:2. Work out the ratio of people who prefer tea to coffee to hot chocolate, giving your answer in its simplest form.

(Total for Question 17 is 4 marks)

In a fruit basket, the ratio of apples to pears is 2:5. There are 35 pieces of fruit in total in the basket. 7 more apples are added to the basket. Work out the new ratio of apples to pears in the basket, giving your answer in its simplest form.

(Total for Question 18 is 4 marks)

The angles in a triangle are in the ratio 2:3:4. Show that none of the angles in the triangle is 90 degrees.

(Total for Question 19 is 3 marks)

Chloe and Dev share a sum of money in the ratio 3:4. Dev receives 24 pounds more than Chloe. Work out the total amount of money shared.

(Total for Question 20 is 4 marks)

Mark scheme · 3.5 Ratio

Question 1

M1 20 / 5 = 4 oe (one share found)
A1 Zara = 4 and Amir = 16 cao
Answer: Zara = 4, Amir = 16

Question 2

B1 C cao
Answer: C) 30

Question 3

M1 45 / 9 = 5 oe (one share found)
A1 20 kg cao
Answer: 20 kg

Question 4

M1 360 / 9 = 40 oe (one share found)
M1 40 x 5 (dep on first M1)
A1 200 pounds cao
Answer: 200 pounds

Question 5

(a) M1 60 / 10 = 6 oe (one share found)
(a) M1 6 x 5 (dep on first M1)
(a) A1 30 cao
(a) Answer: 30 green beads
(b) M1 (2 + 3) x 6 oe, ft from part (a)
(b) A1 30 cao (ft)
(b) Answer: 30 beads

Question 6

(a) M1 21 / 3 = 7 oe (scale factor found)
(a) A1 49 cao
(a) Answer: 49 dogs
(b) B1 70 cao (ft from part (a))
(b) Answer: 70 animals

Question 7

(a) M1 total parts = 2 + 3 + 5 = 10 oe
(a) A1 1/2 oe cao
(a) Answer: 1/2
(b) M1 200 / 10 = 20 oe, ft from part (a)
(b) A1 100 pounds cao (ft)
(b) Answer: 100 pounds

Question 8

M1 960 / 12 = 80 oe (one share found)
M1 multiply each ratio part by 80 (dep on first M1)
A1 Chloe = 160, Mo = 240, Nia = 560, all cao
Answer: Chloe = 160 pounds, Mo = 240 pounds, Nia = 560 pounds

Question 9

M1 scale factor = 5/3 oe
M1 15 x 5/3 (dep on first M1)
A1 25 cm cao
Answer: 25 cm

Question 10

M1 water = 9 x 2.5 = 22.5 oe
M1 2.5 + 22.5 (dep on first M1), or total parts = 10 and 10 x 2.5
A1 25 litres cao
Answer: 25 litres

Question 11

M1 small bag unit price = 1.20 / 500 x 100 = 0.24 pounds per 100 g oe
M1 large bag unit price = 3.15 / 1400 x 100 = 0.225 pounds per 100 g oe
C1 correct conclusion: large bag is better value because 0.225 < 0.24 pounds per 100 g
Answer: Large bag (0.225 pounds per 100 g vs 0.24 pounds per 100 g)

Question 12

M1 24 / 12 = 2 oe (one share found)
M1 defenders = 4 x 2 = 8 oe, then 8/24 x 100 (dep)
A1 awrt 33.3% (exact value 100/3%)
Answer: 33.3% (1 dp); exact value 100/3%

Question 13

M1 sets up 5/15 = x/24 oe, or cross-multiplies 5 x 24 = 15x
A1 x = 8 cao
Answer: x = 8

Question 14

M1 150 / 5 = 30 oe (one share found)
M1 Ravi = 60 and Nia = 90 both found (dep on first M1)
A1 30 pounds cao
Answer: 30 pounds

Question 15

M1 recognises the difference 5 - 3 = 2 parts represents 12 pens oe
M1 1 part = 6, total parts = 5 + 3 = 8 oe (dep on first M1)
A1 48 cao
Answer: 48 pens

Question 16

M1 40 / 5 = 8 oe (one share found)
A1 blue = 24 litres cao
A1 white = 16 litres cao
Answer: blue = 24 litres, white = 16 litres

Question 17

M1 scale tea:coffee so coffee = 12, giving 15:12 oe
M1 scale coffee:hot chocolate so coffee = 12, giving 12:8 oe
A1 15:12:8 cao
C1 ratio correctly labelled and ordered tea : coffee : hot chocolate
Answer: tea : coffee : hot chocolate = 15 : 12 : 8

Question 18

M1 35 / 7 = 5 oe (one share found)
M1 apples = 10 and pears = 25 both found oe
M1 new number of apples = 10 + 7 = 17 (dep)
A1 17:25 cao
Answer: 17 : 25

Question 19

M1 180 / 9 = 20 oe (angle sum of a triangle used)
A1 angles 40, 60 and 80 degrees found (oe)
C1 correct conclusion stated: no angle equals 90 degrees, so the triangle is not right-angled (cso)
Answer: Angles are 40, 60 and 80 degrees; none equals 90, so the triangle is not right-angled.

Question 20

P1 recognises that the difference between the ratio parts, 4 - 3 = 1, represents 24 pounds
M1 total parts = 3 + 4 = 7 oe
M1 7 x 24 (dep on both previous marks)
A1 168 pounds cao
Answer: 168 pounds

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Ratio - Worksheets, Questions and Revision

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3.5 Ratio

Revision notes: Ratio

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

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Question 20