A box contains 9 yellow buttons and 15 pink buttons. Write the ratio of yellow buttons to pink buttons in its simplest form.
A) 9 : 15
B) 5 : 3
C) 3 : 4
D) 3 : 5
E) 1 : 2
(Total for Question 2 is 1 mark)
3
Complete the missing number: 4 : 9 = 20 : ___
A) 25
B) 36
C) 40
D) 45
E) 50
(Total for Question 3 is 1 mark)
4
Which of these ratios is NOT equivalent to 5 : 6?
A) 10 : 12
B) 15 : 18
C) 25 : 30
D) 20 : 23
E) 35 : 42
(Total for Question 4 is 1 mark)
5
Zainab and Callum share 54 sweets in the ratio 2 : 7. Calculate how many sweets Zainab receives.
A) 6
B) 12
C) 18
D) 42
E) 48
(Total for Question 5 is 1 mark)
6
There are 42 pupils in a class. The ratio of pupils who prefer maths to those who prefer art is 4 : 3. Calculate the number of pupils who prefer art.
A) 12
B) 18
C) 24
D) 6
E) 30
(Total for Question 6 is 1 mark)
7
A squash drink is made from concentrate and water in the ratio 1 : 6. Calculate how much water is needed for 30 ml of concentrate.
A) 36
B) 150
C) 180
D) 210
E) 186
(Total for Question 7 is 1 mark)
8
The ratio of oak trees to pine trees in a forest plot is 9 : 16. What percentage of the trees are pine?
A) 36%
B) 56%
C) 60%
D) 64%
E) 69%
(Total for Question 8 is 1 mark)
9
A pancake recipe for 5 people uses 250 g of flour, 300 ml of milk and 125 g of sugar. Rewrite the recipe for 8 people.
(a)Calculate the mass of flour needed for 8 people.(1)
(b)Calculate the volume of milk needed for 8 people.(1)
(c)Calculate the mass of sugar needed for 8 people.(1)
(Total for Question 9 is 3 marks)
10
8 identical erasers cost £3.20. Calculate the cost of 15 of these erasers.
A) £4.80
B) £5.40
C) £6.00
D) £6.40
E) £7.20
(Total for Question 10 is 1 mark)
11
Shop C sells 5 bars of soap for £2.75. Shop D sells 8 bars of soap for £4.00. Work out which shop offers better value for money, showing your working.
(Total for Question 11 is 3 marks)
12
£108 is shared between Elena, Marcus and Priya in the ratio 2 : 4 : 3.
(a)Calculate how much Marcus receives.(2)
(b)Calculate how much more Marcus receives than Elena.(1)
(Total for Question 12 is 3 marks)
13
A map has a scale of 1 : 20 000. Two villages are 9 cm apart on the map. Calculate the real distance between the villages, giving your answer in kilometres.
A) 0.18 km
B) 1.8 km
C) 18 km
D) 1.98 km
E) 0.198 km
(Total for Question 13 is 1 mark)
14
1 mile is equivalent to 8/5 km. Convert a distance of 35 miles into kilometres.
A) 21.9 km
B) 43.75 km
C) 50 km
D) 56 km
E) 70 km
(Total for Question 14 is 1 mark)
15
In a library, the ratio of fiction books to non-fiction books is 5 : 3.
(a)There are 120 fiction books. Calculate the number of non-fiction books.(2)
(b)18 non-fiction books are donated to another library, and no fiction books are added or removed. Calculate the new ratio of fiction to non-fiction books, giving your answer in its simplest form.(2)
(Total for Question 15 is 4 marks)
16
It takes 6 machines working at the same constant rate 10 hours to complete a production run. Calculate how long it would take 4 machines, working at the same rate, to complete an identical production run.
A) 6 hours
B) 6.67 hours
C) 12 hours
D) 15 hours
E) 24 hours
(Total for Question 16 is 1 mark)
17
A train travels at a constant speed and covers 252 km in 3.5 hours. Calculate how far the train would travel in 5 hours at the same speed.
A) 180 km
B) 252 km
C) 300 km
D) 360 km
E) 420 km
(Total for Question 17 is 1 mark)
18
In an orchestra, the ratio of string players to wind players is 8 : 5. There are 21 more string players than wind players. Calculate the total number of players in the orchestra.
A) 21
B) 56
C) 84
D) 91
E) 98
(Total for Question 18 is 1 mark)
19
Harriet, Devon and Sana invest money in a business in the ratio 3 : 4 : 5 respectively. The business makes a profit of £900, which is shared in the same ratio as their investment. Calculate how much more profit Sana receives than Harriet.
A) £75
B) £100
C) £150
D) £225
E) £375
(Total for Question 19 is 1 mark)
20
A photograph measuring 12 cm by 20 cm is enlarged proportionally so that its new height is 30 cm. Calculate the new width of the enlarged photograph.
A) 15 cm
B) 18 cm
C) 20 cm
D) 22 cm
E) 24 cm
(Total for Question 20 is 1 mark)
21
y is directly proportional to x. When x = 8, y = 20. Calculate the value of y when x = 14.
A) 26
B) 28
C) 32.5
D) 35
E) 38.5
(Total for Question 21 is 1 mark)
22
Two numbers are in the ratio 7 : 11. Their sum is 162. Calculate the difference between the two numbers.
A) 18
B) 27
C) 36
D) 63
E) 99
(Total for Question 22 is 1 mark)
23
A metal alloy is made from copper and zinc in the ratio 7 : 2. A metalworker has 54 g of zinc.
(a)Calculate how much copper must be added to the zinc to make the alloy.(2)
(b)Calculate the total mass of alloy produced.(1)
(Total for Question 23 is 3 marks)
24
In a school, the ratio of Year 10 pupils to Year 11 pupils is 7 : 6. The ratio of Year 11 pupils to Year 12 pupils is 2 : 3. Calculate the ratio of Year 10 to Year 11 to Year 12 pupils, giving your answer in its simplest form.
(Total for Question 24 is 3 marks)
25
A sum of money is divided between Olivia and Kofi in the ratio 9 : 5. Olivia receives £68 more than Kofi. Calculate the total sum of money divided between them.
(Total for Question 25 is 4 marks)
26
A sports club has 252 members. The ratio of members who play badminton, tennis and squash is 5 : 3 : 4. The number of badminton players is expected to decrease by 20%, while the total number of members remains 252 and the ratio of tennis to squash (among the unchanged members) stays the same as before. Calculate the new ratio of badminton to tennis to squash, giving your answer in its simplest form.
(Total for Question 26 is 4 marks)
Mark scheme · EP.M6B Ratio and Proportion: Practice Set 2
Question 1
B1 C (4:5) cao
Answer: 4 : 5
Question 2
B1 D (3:5) cao
Answer: 3 : 5
Question 3
B1 D (45) cao
Answer: 45
Question 4
B1 D (20:23) cao
Answer: D) 20 : 23
Question 5
B1 B (12) cao
Answer: 12
Question 6
B1 B (18) cao
Answer: 18
Question 7
B1 C (180 ml) cao
Answer: 180 ml
Question 8
B1 D (64%) cao
Answer: 64%
Question 9
(a) B1 400 g cao
(a) Answer: 400 g
(b) B1 480 ml cao
(b) Answer: 480 ml
(c) B1 200 g cao
(c) Answer: 200 g
Question 10
B1 C (£6.00) cao
Answer: £6.00
Question 11
M1 price per bar at Shop C found: 2.75/5 = 0.55
M1 price per bar at Shop D found: 4.00/8 = 0.50
A1 Shop D offers better value (cao, since £0.50 per bar is less than £0.55 per bar)
Answer: Shop D (£0.50 per bar versus £0.55 per bar at Shop C)
Question 12
(a) M1 total parts found (2 + 4 + 3 = 9) and 108/9 = 12 used, or equivalent method
(a) A1 £48 cao
(a) Answer: £48
(b) B1 £24 (ft from part a: Elena = 2 x their unit value, then Marcus - Elena)
(b) Answer: £24
Question 13
B1 B (1.8 km) cao
Answer: 1.8 km
Question 14
B1 D (56 km) cao
Answer: 56 km
Question 15
(a) M1 unit value found: 120/5 = 24, or equivalent method
(a) A1 72 cao
(a) Answer: 72
(b) M1 new number of non-fiction books found (ft from part a): 72 - 18 = 54
(b) A1 20 : 9 oe cao
(b) Answer: 20 : 9
Question 16
B1 D (15 hours) cao
Answer: 15 hours
Question 17
B1 D (360 km) cao
Answer: 360 km
Question 18
B1 D (91) cao
Answer: 91
Question 19
B1 C (£150) cao
Answer: £150
Question 20
B1 B (18 cm) cao
Answer: 18 cm
Question 21
B1 D (35) cao
Answer: 35
Question 22
B1 C (36) cao
Answer: 36
Question 23
(a) M1 unit value found: 54/2 = 27
(a) A1 189 g cao
(a) Answer: 189 g
(b) B1 243 g (ft from part a: 54 + their copper mass)
(b) Answer: 243 g
Question 24
M1 finds a common value for Year 11 in both ratios (e.g. scales 2:3 to 6:9, using the LCM of 6 and 2, which is 6)
M1 dep: combines to give 7 : 6 : 9
A1 7 : 6 : 9 cao (already in simplest form, HCF = 1)
Answer: 7 : 6 : 9
Question 25
M1 difference in parts found: 9 - 5 = 4
M1 dep: unit value found: 68/4 = 17
M1 dep: total parts found (9 + 5 = 14) and their 17 x 14
A1 £238 cao
Answer: £238
Question 26
M1 original numbers found: total parts 5 + 3 + 4 = 12, unit value 252/12 = 21, so badminton = 105, tennis = 63, squash = 84
M1 dep: new badminton number found: 105 x 0.8 = 84
M1 dep: remaining members (252 - 84 = 168) split in the ratio 3:4 (unit value 168/7 = 24), giving tennis = 72 and squash = 96