Ratio and Proportion - Worksheets, Questions and Revision

20 original exam-style questions - 9 pages of questions with a full mark scheme - free printable PDF.

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13+ · Mathematics

CE.M3 Ratio and Proportion

ISEB CE CE.M3 · Calculator allowed · about 85 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write each ratio in its simplest form.
(a)18:24(1)
(b)42:63(1)
(Total for Question 1 is 2 marks)
2
A fruit bowl contains 12 apples and 20 oranges, and no other fruit.
(a)Write the ratio of apples to oranges in its simplest form.(1)
(b)What fraction of the fruit in the bowl are apples? Give your answer in its simplest form.(2)
(Total for Question 2 is 3 marks)
3
Amy and Ben share 45 sweets in the ratio 4:5.
(a)Find the value of one share.(1)
(b)Work out how many sweets Ben receives.(2)
(Total for Question 3 is 3 marks)
4
For each question, circle the letter next to the correct answer.
(a)Which ratio is equivalent to 2:3?(1)
  • A) 4:5
  • B) 6:9
  • C) 8:10
  • D) 10:12
(b)Simplify the ratio 0.4:0.6 to a ratio of whole numbers in its simplest form.(1)
  • A) 2:3
  • B) 4:6
  • C) 3:2
  • D) 6:4
(c)A bag contains counters in the ratio 3:7. What fraction of the counters make up the larger group?(1)
  • A) 3/10
  • B) 7/10
  • C) 7/3
  • D) 3/7
(Total for Question 4 is 3 marks)
5
Write each ratio in the form 1:n.
(a)4:20(1)
(b)8:3(2)
(Total for Question 5 is 3 marks)
6
A recipe for 6 people uses 300 grams of flour, 150 grams of sugar and 3 eggs.
(a)Fatima wants to make the recipe for 9 people. Work out how much flour she needs.(2)
(b)Kwame wants to make the recipe for 15 people. Work out how much sugar he needs.(2)
(Total for Question 6 is 4 marks)
7
At a rescue centre, the ratio of cats to dogs is 5:7. There are 35 dogs at the centre.
(a)Calculate how many cats are at the centre.(2)
(b)Work out the total number of animals at the centre.(1)
(Total for Question 7 is 3 marks)
8
90 pounds is shared between Priya, Kwame and Zara in the ratio 2:3:4.
(a)Find the value of one share.(1)
(b)Work out how much money each person receives.(3)
(Total for Question 8 is 4 marks)
9
A map has a scale of 1:25000.
(a)The distance between two villages on the map is 6 cm. Work out the real distance between the villages, in km.(3)
(b)Two towns are 8 km apart in real life. Work out the distance between them on the map, in cm.(2)
(Total for Question 9 is 5 marks)
10
A 750 gram box of cereal costs 2.85 pounds. A 1.2 kilogram box of the same cereal costs 4.32 pounds.
(a)Calculate the cost per 100 grams for each box.(2)
(b)State, with a reason, which box gives better value for money.(2)
(Total for Question 10 is 4 marks)
11
At a school, the ratio of Year 9 students to Year 10 students is 4:5. The ratio of Year 10 students to Year 11 students is 3:2.
(a)Find the ratio of Year 9 students to Year 10 students to Year 11 students, giving your answer in its simplest form.(3)
(b)There are 108 Year 9 students. Work out the number of Year 11 students.(2)
(Total for Question 11 is 5 marks)
12
The exchange rate between pounds sterling and euros is 1 pound = 1.17 euros.
(a)Convert 250 pounds to euros.(2)
(b)Convert 351 euros to pounds sterling.(2)
(Total for Question 12 is 4 marks)
13
A car travels at a constant speed. It travels 108 miles in 2 hours.
(a)Work out the speed of the car, in miles per hour.(1)
(b)Using a proportion method, work out how long the car takes to travel 270 miles at the same speed.(3)
(Total for Question 13 is 4 marks)
14
At the same time of day, a 1.8 metre tall pole casts a shadow of 2.4 metres. A nearby tree casts a shadow of 12 metres.
(a)Find the ratio of height to shadow length for the pole, in its simplest form.(2)
(b)Use this ratio to find the height of the tree.(2)
(Total for Question 14 is 4 marks)
15
A business profit of 7200 pounds is shared between three partners, Oliver, Priya and Zara, in the ratio 3:4:5.
(a)Find the value of one share.(1)
(b)Work out how much money each partner receives.(2)
(c)Zara donates 15% of her share to charity. Calculate how much she donates.(1)
(Total for Question 15 is 4 marks)
16
The ratio of Sanjay's age to his sister Meera's age is 3:5. In 6 years' time, the ratio of their ages will be 2:3.
(a)Using x for the common multiplier, write expressions for Sanjay's current age and Meera's current age.(1)
(b)Form an equation and solve it to find the value of x.(3)
(c)State Sanjay's current age.(1)
(Total for Question 16 is 5 marks)
17
Two similar cylinders have heights in the ratio 2:5.
(a)Write the ratio of the volumes of the two cylinders.(2)
(b)The smaller cylinder has a volume of 96 cm3. Find the volume of the larger cylinder.(2)
(c)The smaller cylinder has a surface area of 60 cm2. Find the surface area of the larger cylinder.(2)
(Total for Question 17 is 6 marks)
18
The time taken to build a wall is inversely proportional to the number of builders working, assuming they all work at the same constant rate. 4 builders take 15 days to build a wall.
(a)Calculate how long 6 builders would take to build the same wall.(3)
(b)The wall must now be finished in 5 days. Calculate how many builders are needed.(2)
(Total for Question 18 is 5 marks)
19
A charity raises money for two causes, Cause A and Cause B, in the ratio 5:3. Cause A receives 1250 pounds more than Cause B.
(a)Using x for one share, form an equation and solve it to find the value of x.(2)
(b)Find the total amount of money raised for both causes.(2)
(Total for Question 19 is 4 marks)
20
A shop sells two types of coffee. Colombian coffee costs 8 pounds per kg and Kenyan coffee costs 11 pounds per kg. A blend is made by mixing Colombian and Kenyan coffee in the ratio 5:2 by mass.
(a)Calculate the cost of 1 kg of the blend, giving your answer to the nearest penny.(3)
(b)A cafe needs 21 kg of the blend. Calculate the mass of Colombian coffee and the mass of Kenyan coffee required.(2)
(Total for Question 20 is 5 marks)
Mark scheme · CE.M3 Ratio and Proportion

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