A biscuit tin contains 20 chocolate biscuits and 12 plain biscuits. Write the ratio of chocolate biscuits to plain biscuits in its simplest form.
(Total for Question 2 is 1 mark)
3
Complete the missing number: 4 : 7 = 24 : ___
(Total for Question 3 is 1 mark)
4
Which of these ratios is NOT equivalent to 6 : 11?
A) 12 : 22
B) 18 : 33
C) 24 : 44
D) 30 : 56
(Total for Question 4 is 1 mark)
5
Simplify the ratio 0.8 : 3.2 to its simplest whole-number form.
(Total for Question 5 is 1 mark)
6
Write the ratio 750 g : 2 kg in its simplest whole-number form.
(Total for Question 6 is 1 mark)
7
Kwame and Elif share 96 sweets in the ratio 5 : 3. Calculate how many sweets Elif receives.
(Total for Question 7 is 2 marks)
8
There are 35 pupils in a class. The ratio of pupils who walk to school to those who do not walk is 2 : 5. Calculate the number of pupils who walk to school.
(Total for Question 8 is 2 marks)
9
A fruit bowl contains lemon muffins and orange muffins in the ratio 9 : 11. Calculate what percentage of the muffins are lemon muffins.
(Total for Question 9 is 2 marks)
10
y is directly proportional to x. When x = 9, y = 24. Calculate the value of y when x = 15.
(Total for Question 10 is 2 marks)
11
11 identical protractors cost £9.90 in total. Calculate the cost of 4 of these protractors.
(Total for Question 11 is 2 marks)
12
A cyclist rides at a constant speed and covers 42 km in 3 hours. At this speed, how far would the cyclist travel in 5 hours?
A) 60 km
B) 65 km
C) 70 km
D) 75 km
(Total for Question 12 is 1 mark)
13
A curry recipe for 4 people uses 500 g of chicken, 2 stock cubes, 4 chillies and 250 ml of cream. The recipe is scaled up for 10 people.
(a)Calculate the mass of chicken needed for 10 people.(1)
(b)Calculate the number of stock cubes needed for 10 people.(1)
(c)Calculate the number of chillies needed for 10 people.(1)
(d)Calculate the volume of cream needed for 10 people.(1)
(Total for Question 13 is 4 marks)
14
Shop G sells a 900 g jar of coffee for £8.10. Shop H sells a 1.5 kg jar of the same coffee for £12.75. Work out which shop offers better value for money, showing your working.
(Total for Question 14 is 3 marks)
15
It takes 6 identical taps, running at the same constant rate, 10 hours to fill a swimming pool. Calculate how long it would take 4 of these taps, running at the same rate, to fill the same pool.
(Total for Question 15 is 3 marks)
16
A map has a scale of 1 : 40 000. Two lighthouses are 6.25 cm apart on the map. Calculate the real distance between them, giving your answer in kilometres.
(Total for Question 16 is 3 marks)
17
A prize fund of £480 is shared between three quiz teams, the Eagles, the Falcons and the Hawks, in the ratio 5 : 4 : 3. Calculate how much more money the Eagles receive than the Hawks.
(Total for Question 17 is 3 marks)
18
A poster measuring 30 cm by 42 cm is enlarged proportionally so that its new width is 45 cm. Calculate the new height of the poster.
(Total for Question 18 is 3 marks)
19
Priya, Reuben and Aisha invest money in a bakery in the ratio 5 : 6 : 9 respectively. The bakery makes a profit of £1200, which is shared in the same ratio as their investment. Calculate how much profit Reuben receives.
(Total for Question 19 is 3 marks)
20
At a chess club, the ratio of adult members to junior members is 7 : 4. There are 21 more adult members than junior members. Calculate the total number of members in the club.
(Total for Question 20 is 3 marks)
21
In a fruit bowl, the ratio of apples to pears is 3 : 2. The ratio of pears to plums is 5 : 4. Calculate the ratio of apples to pears to plums, giving your answer in its simplest form.
(Total for Question 21 is 3 marks)
22
Two numbers are in the ratio 4 : 9. Their sum is 156. Calculate the positive difference between the two numbers.
(Total for Question 22 is 3 marks)
23
A sum of money is shared between Farah and Idris in the ratio 8 : 5. Farah then gives Idris £39, after which they have equal amounts of money. Calculate the total sum of money shared between them originally.
(Total for Question 23 is 4 marks)
24
It takes 9 painters, working at the same constant rate, 12 days to paint a school hall. The school wants the job finished in 4 days. Calculate how many painters, working at the same rate, are needed to finish the job in 4 days.
(Total for Question 24 is 3 marks)
25
A fun run has 700 T-shirts allocated to three sizes, small, medium and large, in the ratio 4 : 9 : 7. Before the event, 40 medium T-shirts are reallocated equally between small and large, while the total number of T-shirts stays at 700. Calculate the new ratio of small to medium to large T-shirts, giving your answer in its simplest form.
(Total for Question 25 is 4 marks)
26
A recipe for 6 people uses 450 g of rice. Yusuf has 1 kg of rice and wants to use exactly 80% of it to make the recipe, giving as many whole servings as possible. Calculate the greatest number of whole people the recipe can serve using 80% of Yusuf's rice.
(Total for Question 26 is 4 marks)
Mark scheme · EP.M67 Ratio and Proportion: Practice Set 4
Question 1
B1 A (2 : 3) cao
Answer: A) 2 : 3
Question 2
B1 5 : 3 oe cao
Answer: 5 : 3
Question 3
B1 42 cao
Answer: 42
Question 4
B1 D (30:56) cao
Answer: D) 30 : 56
Question 5
B1 1 : 4 oe cao
Answer: 1 : 4
Question 6
B1 3 : 8 oe cao
Answer: 3 : 8
Question 7
M1 total parts found (5 + 3 = 8) and unit value found: 96/8 = 12
A1 36 cao
Answer: 36
Question 8
M1 total parts found (2 + 5 = 7) and unit value found: 35/7 = 5
A1 10 cao
Answer: 10
Question 9
M1 total parts found (9 + 11 = 20) and fraction 9/20 set up, or equivalent method
A1 45% oe cao
Answer: 45%
Question 10
M1 scale factor found: 15/9 = 5/3, or constant of proportionality k = 24/9, or equivalent method
A1 40 cao
Answer: 40
Question 11
M1 unit cost found: 9.90/11 = 0.90
A1 £3.60 cao
Answer: £3.60
Question 12
B1 C (70 km) cao
Answer: C) 70 km
Question 13
(a) B1 1250 g oe (1.25 kg) cao
(a) Answer: 1250 g
(b) B1 5 cao
(b) Answer: 5
(c) B1 10 cao
(c) Answer: 10
(d) B1 625 ml cao
(d) Answer: 625 ml
Question 14
M1 price per 100 g at Shop G found: (8.10/900) x 100 = 0.90
M1 price per 100 g at Shop H found: (12.75/1500) x 100 = 0.85
A1 Shop H offers better value cao (£0.85 per 100 g versus £0.90 per 100 g at Shop G)
Answer: Shop H (£0.85 per 100 g versus £0.90 per 100 g at Shop G)
Question 15
M1 total 'tap-hours' found: 6 x 10 = 60
M1 dep: their 60/4
A1 15 hours cao
Answer: 15 hours
Question 16
M1 real distance found in cm: 6.25 x 40 000 = 250 000
M1 dep: converts their 250 000 cm to metres then kilometres (250 000/100 = 2500 m, then /1000)
A1 2.5 km cao
Answer: 2.5 km
Question 17
M1 total parts found (5 + 4 + 3 = 12) and unit value found: 480/12 = 40
M1 dep: Eagles' share and Hawks' share found (5 x 40 = 200, 3 x 40 = 120)
A1 £80 cao
Answer: £80
Question 18
M1 scale factor found: 45/30 = 1.5
M1 dep: their 1.5 x 42
A1 63 cm cao
Answer: 63 cm
Question 19
M1 total parts found (5 + 6 + 9 = 20) and unit value found: 1200/20 = 60
M1 dep: their 6 x 60
A1 £360 cao
Answer: £360
Question 20
M1 difference in parts found (7 - 4 = 3) and unit value found (21/3 = 7)
M1 dep: total parts found (7 + 4 = 11) and their 7 x 11
A1 77 cao
Answer: 77
Question 21
M1 finds a common value for pears in both ratios (e.g. scales 3:2 to 15:10 and 5:4 to 10:8, using the LCM of 2 and 5, which is 10)
M1 dep: combines to give 15 : 10 : 8
A1 15 : 10 : 8 cao (already in simplest form, HCF = 1)
Answer: 15 : 10 : 8
Question 22
M1 total parts found (4 + 9 = 13) and unit value found: 156/13 = 12
M1 dep: the two numbers found (4 x 12 = 48, 9 x 12 = 108)
A1 60 cao
Answer: 60
Question 23
M1 original shares written as 8k and 5k (or equivalent unitary method)
M1 equation set up for equal amounts after the transfer: 8k - 39 = 5k + 39
dM1 dep: solves to find k = 26
A1 £338 cao
Answer: £338
Question 24
M1 total 'painter-days' found: 9 x 12 = 108
M1 dep: their 108/4
A1 27 painters cao
Answer: 27 painters
Question 25
M1 original numbers found: total parts 4 + 9 + 7 = 20, unit value 700/20 = 35, so small = 140, medium = 315, large = 245
M1 dep: 40 medium T-shirts split equally, so 20 added to small and 20 to large
M1 dep: new numbers found (small = 160, medium = 275, large = 265) and simplified using HCF 5
A1 32 : 55 : 53 cao
Answer: 32 : 55 : 53
Question 26
M1 80% of 1000 g found: 800 g
M1 dep: rice needed per person found: 450/6 = 75 g
M1 dep: their 800/75 = 10.666...
A1 10 (people) cao, rounded down since only whole servings are possible