⚖️ Maths: Ratio and Proportion

1. What is the simplest form of the ratio 10:15?

1. 2:3
2. 5:10
3. 1:2
4. 3:2

Divide both parts by their highest common factor, 5, so 10:15 becomes 2:3. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

2. To simplify a ratio to its lowest terms, what must you divide all of its parts by?

1. Their highest common factor
2. Their lowest common multiple
3. The first part of the ratio
4. The sum of all the parts

A ratio is simplified by dividing every part by their highest common factor. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

3. A fruit drink is made by mixing 8 parts water with 12 parts juice. Written in its simplest form, what is the ratio of water to juice?

1. 2:3
2. 4:6
3. 8:12
4. 3:2

Dividing both parts by the highest common factor 4 gives 8:12 = 2:3. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

4. In a car park there are 24 cars and 18 vans. What is the ratio of cars to vans in its simplest form?

1. 4:3
2. 3:4
3. 24:18
4. 6:4

The highest common factor of 24 and 18 is 6, so 24:18 simplifies to 4:3. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

5. A recipe uses 250 g of flour to 100 g of butter. What is the ratio of flour to butter in its simplest form?

1. 5:2
2. 2:5
3. 25:10
4. 250:100

Dividing both quantities by the highest common factor 50 gives 250:100 = 5:2. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

6. A length of 1.2 m of ribbon is cut from a 3 m roll. What is the ratio of the cut piece to the whole roll in its simplest form?

1. 2:5
2. 12:30
3. 1:3
4. 2:3

Working in the same units, 1.2 m : 3 m is 120:300, which divides by 60 to give 2:5. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

7. Which statement correctly describes what a ratio compares?

1. It compares two or more quantities measured in the same units
2. It always compares a part to the whole amount
3. It compares quantities that must be in different units
4. It compares a quantity to 100

A ratio compares two or more quantities measured in the same units, comparing parts to other parts. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

8. Which of these ratios is equivalent to 1:4?

1. 2:8
2. 4:1
3. 1:8
4. 2:4

Multiplying both parts of 1:4 by 2 gives 2:8, which represents the same proportion. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (equivalent ratios))

9. The ratio 4:10 is to be written in the unitary form 1:n. What is the value of n?

1. 2.5
2. 6
3. 2
4. 4

Dividing both parts by the first part (4) gives 1:2.5. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (1:n ratios))

10. A mortar mix uses sand and cement in the ratio 5:1. Written as a scale of cement to sand in the form 1:n, what is the value of n?

1. 5
2. 6
3. 0.2
4. 1

Cement to sand is 1:5, so dividing both parts by the first part keeps it as 1:5, giving n = 5. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (1:n ratios))

11. A scale model is made at a scale of 1:50. On the model a wall measures 3 cm. What is the actual length of the wall?

1. 1.5 m
2. 150 m
3. 15 cm
4. 0.5 m

On a 1:50 scale, actual length is 3 cm x 50 = 150 cm, which is 1.5 m. (DfE, 'Functional Skills subject content – mathematics' (gov.uk, 2018), Level 2 statement 18 (scale drawings))

12. To share £200 between two people in the ratio 3:2, how much does the person with the larger share receive?

1. £120
2. £80
3. £100
4. £133

There are 3+2 = 5 parts; 200 divided by 5 is 40, so the larger share is 3 x 40 = £120. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

13. In the ratio 3:2 there are 5 parts in total. What fraction of the whole is the first quantity?

1. 3/5
2. 3/2
3. 2/5
4. 1/3

The first quantity is 3 out of 5 total parts, so the fraction is 3/5. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

14. In a ratio of 3:2, the first quantity is 3/5 of the whole. What is this as a percentage?

1. 60%
2. 30%
3. 40%
4. 65%

3/5 is equal to 0.6, which is 60%. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

15. Which statement best explains the difference between a ratio and a proportion?

1. A ratio compares parts to other parts, while a proportion compares a part to the whole
2. A ratio compares a part to the whole, while a proportion compares parts to other parts
3. A ratio and a proportion always give the same value
4. A proportion can never be written as a percentage

A ratio compares parts to other parts, whereas a proportion is expressed as a fraction, decimal or percentage of the whole. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

16. A class is made up of boys and girls in the ratio 2:3. What percentage of the class are girls?

1. 60%
2. 40%
3. 30%
4. 66%

There are 5 parts in total and girls are 3 of them, so 3/5 = 60%. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

17. A drink is mixed with squash and water in the ratio 1:4. What fraction of the mixture is squash?

1. 1/5
2. 1/4
3. 4/5
4. 1/3

There are 1+4 = 5 parts in total, and squash is 1 part, so the fraction is 1/5. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

18. In a car park the ratio of red cars to other cars is 1:4. What percentage of the cars are red?

1. 20%
2. 25%
3. 40%
4. 80%

There are 5 parts in total and red cars are 1 part, so 1/5 = 20%. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

19. In a fruit basket the ratio of apples to oranges to pears is 3:2:5. What percentage of the fruit are oranges?

1. 20%
2. 30%
3. 50%
4. 25%

There are 3+2+5 = 10 parts in total and oranges are 2, so 2/10 = 20%. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio versus proportion))

20. A ratio is given as 1:4. Written as an equivalent ratio out of 100, which is correct?

1. 25:100
2. 20:100
3. 4:100
4. 1:100

Multiplying both parts of 1:4 by 25 gives 25:100, an equivalent ratio. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (equivalent ratios))

21. In inverse proportion, what happens to one quantity as the other increases?

1. It decreases so that their product stays constant
2. It increases by the same amount
3. It stays exactly the same
4. It also increases in the same ratio

In inverse proportion, as one quantity increases the other decreases so that their product remains constant. (DfE, 'Functional Skills subject content – mathematics' (gov.uk, 2018), Level 2 statement 11 (inverse proportion))

22. It takes 4 people 6 days to complete a job. Assuming they all work at the same rate, how long would 3 people take?

1. 8 days
2. 6 days
3. 4.5 days
4. 12 days

The total work is 4 x 6 = 24 person-days, so 3 people take 24 divided by 3 = 8 days. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (inverse proportion))

23. If 2 painters take 12 hours to paint a hall, how long would 4 painters working at the same rate take?

1. 6 hours
2. 24 hours
3. 8 hours
4. 3 hours

The total work is 2 x 12 = 24 painter-hours, so 4 painters take 24 divided by 4 = 6 hours. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (inverse proportion))

24. A supply of food lasts 5 cows for 8 days. How long would the same supply last 4 cows?

1. 10 days
2. 6.4 days
3. 9 days
4. 12 days

The total food is 5 x 8 = 40 cow-days, so for 4 cows it lasts 40 divided by 4 = 10 days. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (inverse proportion))

25. For two quantities in inverse proportion, when one quantity is doubled, what happens to the other?

1. It is halved
2. It is doubled
3. It stays the same
4. It is reduced by 2

In inverse proportion their product is constant, so doubling one quantity halves the other. (DfE, 'Functional Skills subject content – mathematics' (gov.uk, 2018), Level 2 statement 11 (inverse proportion))

26. A water tank is filled by 6 identical pumps in 90 minutes. How long would it take 5 of these pumps to fill the same tank?

1. 108 minutes
2. 75 minutes
3. 96 minutes
4. 120 minutes

The total work is 6 x 90 = 540 pump-minutes, so 5 pumps take 540 divided by 5 = 108 minutes. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (inverse proportion))

27. A coach travelling at 60 km/h completes a journey in 3 hours. If the speed is increased to 90 km/h, how long will the same journey take?

1. 2 hours
2. 2.5 hours
3. 4.5 hours
4. 1.5 hours

Distance is constant at 60 x 3 = 180 km, so at 90 km/h the time is 180 divided by 90 = 2 hours; speed and time are in inverse proportion. (DfE, 'Functional Skills subject content – mathematics' (gov.uk, 2018), Level 2 statement 11 (inverse proportion))

28. Which everyday situation is an example of inverse proportion?

1. The more workers there are, the less time a fixed job takes
2. The more hours you work, the more pay you receive at a fixed rate
3. The more litres of petrol you buy, the higher the total cost
4. The more metres of fabric you buy, the greater the total length

More workers completing a fixed job in less time is inverse proportion, because people multiplied by time stays constant. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (inverse proportion))

29. When sharing a quantity in a given ratio, what is the correct first step?

1. Add the parts of the ratio together to find the total number of parts
2. Subtract the smaller part from the larger part
3. Multiply the two parts of the ratio together
4. Divide the quantity by the larger part only

You first add the parts of the ratio to find the total number of parts, then divide the quantity by that total to find the value of one part. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (ratio and proportion))

30. A sum of £200 is to be shared between two people in the ratio 3:2. How much does each person receive?

1. £120 and £80
2. £100 and £100
3. £150 and £50
4. £130 and £70

The parts total 3+2=5, so one part is 200÷5=£40; the shares are 3×40=£120 and 2×40=£80. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (sharing in a ratio))

31. £60 is shared in the ratio 1:5. What is the smaller share?

1. £10
2. £12
3. £6
4. £15

The parts total 1+5=6, so one part is 60÷6=£10, which is the smaller share. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (sharing in a ratio))

32. A recipe mix of 750 g is made by combining flour and sugar in the ratio 4:1. How much sugar is used?

1. 150 g
2. 187.5 g
3. 250 g
4. 100 g

The parts total 4+1=5, so one part is 750÷5=150 g; the sugar is 1×150=150 g. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (sharing in a ratio))

33. £540 is divided between three charities in the ratio 2:3:4. How much does the charity with the largest share receive?

1. £240
2. £180
3. £120
4. £270

The parts total 2+3+4=9, so one part is 540÷9=£60; the largest share is 4×60=£240. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (sharing in a ratio))

34. A bag of 96 sweets is shared between Amir and Beth in the ratio 5:3. How many more sweets does Amir get than Beth?

1. 24
2. 12
3. 36
4. 18

The parts total 5+3=8, so one part is 96÷8=12; Amir gets 5×12=60 and Beth gets 3×12=36, a difference of 24. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (sharing in a ratio))

35. Concrete is made by mixing cement and sand in the ratio 1:6. To make 35 kg of concrete, how much sand is needed?

1. 30 kg
2. 6 kg
3. 5 kg
4. 29 kg

The parts total 1+6=7, so one part is 35÷7=5 kg; the sand is 6×5=30 kg. (Pearson, Functional Skills Maths Level 2, Chapter 3 Learner Materials (sharing in a ratio))