Which of these is the simplified form of the ratio 28 : 35?
A) 4 : 5
B) 7 : 8
C) 4 : 7
D) 2 : 3
(Total for Question 2 is 1 mark)
3
A bakery tray holds 14 blueberry muffins and 21 chocolate muffins. Write the ratio of blueberry muffins to chocolate muffins in its simplest form.
(Total for Question 3 is 1 mark)
4
Which of these ratios is equivalent to 5 : 6?
A) 10 : 11
B) 15 : 18
C) 20 : 25
D) 25 : 36
(Total for Question 4 is 1 mark)
5
Complete the missing number: 7 : 9 = ___ : 63
(Total for Question 5 is 1 mark)
6
On a school trip, the ratio of teachers to pupils must be at least 1 : 8. If 6 teachers go on the trip, what is the maximum number of pupils allowed?
A) 14
B) 42
C) 48
D) 56
(Total for Question 6 is 1 mark)
7
A publisher prints fiction and non-fiction books in the ratio 5 : 3. Calculate how many of each type of book are printed if the total print run is 96 books.
(Total for Question 7 is 2 marks)
8
A youth club has 63 members. The ratio of members aged under 13 to members aged 13 and over is 2 : 5. Calculate the number of members aged 13 and over.
(Total for Question 8 is 2 marks)
9
The ratio of red counters to green counters in a jar is 3 : 5. There are 40 counters in the jar altogether. How many green counters are there?
A) 15
B) 20
C) 24
D) 25
(Total for Question 9 is 1 mark)
10
9 identical rulers cost £5.85 in total. Calculate the cost of 4 of these rulers.
(Total for Question 10 is 2 marks)
11
A decorator mixes blue paint and white paint in the ratio 3 : 8 to make a particular shade of grey. Calculate how much white paint is needed for 45 ml of blue paint.
(Total for Question 11 is 2 marks)
12
£1 is worth $1.25. Calculate how many dollars a tourist receives for £68.
(Total for Question 12 is 2 marks)
13
A cake recipe for 8 people uses 200 g of butter, 320 g of sugar, 4 eggs and 360 g of flour. Rewrite the recipe for 12 people.
(a)Calculate the mass of butter needed for 12 people.(1)
(b)Calculate the mass of sugar needed for 12 people.(1)
(c)Calculate the number of eggs needed for 12 people.(1)
(d)Calculate the mass of flour needed for 12 people.(1)
(Total for Question 13 is 4 marks)
14
Cereal A costs £2.40 for a 750 g box. Cereal B costs £1.75 for a 500 g box. Work out which cereal offers better value for money, showing your working.
(Total for Question 14 is 3 marks)
15
A map has a scale of 1 : 20 000. Two campsites are 8.5 cm apart on the map. Calculate the real distance between the campsites, giving your answer in kilometres.
(Total for Question 15 is 3 marks)
16
A bag of mixed nuts contains almonds, cashews and peanuts in the ratio 2 : 3 : 5. Calculate what fraction of the nuts in the bag are peanuts.
(Total for Question 16 is 2 marks)
17
A ribbon of length 84 cm is cut into three pieces in the ratio 2 : 3 : 7. Calculate the length of the longest piece.
(Total for Question 17 is 2 marks)
18
A train travels at a constant speed and covers 154 km in 3.5 hours. Calculate how far the train would travel in 5 hours at the same speed.
(Total for Question 18 is 3 marks)
19
It takes 6 machines, working at the same constant rate, 10 hours to complete an order. Calculate how long it would take 4 machines, working at the same rate, to complete an identical order.
(Total for Question 19 is 3 marks)
20
A fruit squash is made from concentrate and water in the ratio 1 : 6. A jug holds 2.8 litres of squash in total. Calculate how much concentrate is in the jug.
(Total for Question 20 is 2 marks)
21
A printer prints pages at a constant rate. It prints 156 pages in 12 minutes. Calculate how many pages it would print in 20 minutes at the same rate.
(Total for Question 21 is 2 marks)
22
Two numbers are in the ratio 5 : 8. Their difference is 39. Calculate the sum of the two numbers.
(Total for Question 22 is 3 marks)
23
A sum of money is shared between Ade and Bo in the ratio 7 : 5. Ade then gives Bo £24, after which they have equal amounts of money. Calculate the original total sum of money shared between them.
(Total for Question 23 is 4 marks)
24
A company's profit of £900 is divided between three partners, Owen, Priya and Zack, in the ratio 4 : 5 : 6. Zack donates one third of his share to charity and keeps the rest. Calculate how much money Zack keeps.
(Total for Question 24 is 3 marks)
25
In a factory, the ratio of day-shift workers to night-shift workers is 7 : 3. The ratio of night-shift workers to weekend-only workers is 2 : 5. Calculate the ratio of day-shift to night-shift to weekend-only workers, giving your answer in its simplest form.
(Total for Question 25 is 3 marks)
26
A sum of money is divided between Grace and Kwame in the ratio 9 : 4. Grace receives £70 more than Kwame. Calculate the total sum of money.
(Total for Question 26 is 4 marks)
27
A stadium has 450 seats reserved for home fans, away fans and neutral fans in the ratio 7 : 2 : 1. Before kick-off, 30 neutral seats are reallocated equally between home fans and away fans, while the total number of reserved seats stays at 450. Calculate the new ratio of home to away to neutral seats, giving your answer in its simplest form.
(Total for Question 27 is 4 marks)
Mark scheme · EP.M40 Ratio and Proportion Depth
Question 1
B1 3 : 4 oe cao
Answer: 3 : 4
Question 2
B1 A (4:5) cao
Answer: A) 4 : 5
Question 3
B1 2 : 3 oe cao
Answer: 2 : 3
Question 4
B1 B (15:18) cao
Answer: B) 15 : 18
Question 5
B1 49 cao
Answer: 49
Question 6
B1 C (48) cao
Answer: C) 48
Question 7
M1 total parts found (5 + 3 = 8) and 96/8 = 12 used, or equivalent method
A1 fiction = 60 and non-fiction = 36 cao
Answer: Fiction = 60, non-fiction = 36
Question 8
M1 total parts found (2 + 5 = 7) and 63/7 = 9 used, or equivalent method
A1 45 cao
Answer: 45
Question 9
B1 D (25) cao
Answer: D) 25
Question 10
M1 cost of 1 ruler found: 5.85/9 = 0.65
A1 £2.60 cao
Answer: £2.60
Question 11
M1 scale factor found: 45/3 = 15, or equivalent method
A1 120 ml cao
Answer: 120 ml
Question 12
M1 68 x 1.25 set up, or equivalent method
A1 $85 cao
Answer: $85
Question 13
(a) B1 300 g cao
(a) Answer: 300 g
(b) B1 480 g cao
(b) Answer: 480 g
(c) B1 6 eggs cao
(c) Answer: 6 eggs
(d) B1 540 g cao
(d) Answer: 540 g
Question 14
M1 price per 100 g for Cereal A found: 2.40/7.5 = 0.32 (32p)
M1 price per 100 g for Cereal B found: 1.75/5 = 0.35 (35p)
A1 Cereal A offers better value (cao, since 32p per 100 g is less than 35p per 100 g)
Answer: Cereal A (32p per 100 g versus 35p per 100 g for Cereal B)
Question 15
M1 real distance found in cm: 8.5 x 20 000 = 170 000
M1 dep: converts their 170 000 cm to metres then kilometres (170 000 / 100 = 1700 m, then / 1000)
A1 1.7 km cao
Answer: 1.7 km
Question 16
M1 total parts found (2 + 3 + 5 = 10)
A1 1/2 oe cao
Answer: 1/2
Question 17
M1 total parts found (2 + 3 + 7 = 12) and 84/12 = 7 used, or equivalent method
A1 49 cm cao
Answer: 49 cm
Question 18
M1 speed found: 154/3.5 = 44 km/h
M1 dep: their 44 x 5
A1 220 km cao
Answer: 220 km
Question 19
M1 total machine-hours found: 6 x 10 = 60
M1 dep: their 60/4
A1 15 hours cao
Answer: 15 hours
Question 20
M1 total parts found (1 + 6 = 7) and 2.8/7 = 0.4 used, or equivalent method
A1 0.4 litres oe (400 ml) cao
Answer: 0.4 litres (400 ml)
Question 21
M1 rate found: 156/12 = 13 pages per minute
A1 260 pages cao
Answer: 260 pages
Question 22
M1 difference in parts found (8 - 5 = 3) and unit value found: 39/3 = 13
M1 dep: the two numbers found (5 x 13 = 65, 8 x 13 = 104)
A1 169 cao
Answer: 169
Question 23
M1 sets up equation using unit value x: 7x - 24 = 5x + 24
M1 dep: solves to find x = 24
M1 dep: original amounts found (Ade = 7 x 24 = 168, Bo = 5 x 24 = 120)
A1 £288 cao
Answer: £288
Question 24
M1 total parts found (4 + 5 + 6 = 15) and unit value found: 900/15 = 60
M1 dep: Zack's share found: 6 x 60 = 360
A1 £240 cao
Answer: £240
Question 25
M1 finds a common value for night-shift workers in both ratios (e.g. scales 7:3 to 14:6 and 2:5 to 6:15, using the LCM of 3 and 2, which is 6)
M1 dep: combines to give 14 : 6 : 15
A1 14 : 6 : 15 cao (already in simplest form, HCF = 1)
Answer: 14 : 6 : 15
Question 26
M1 difference in parts found: 9 - 4 = 5
M1 dep: unit value found: 70/5 = 14
M1 dep: total parts found (9 + 4 = 13) and their 14 x 13
A1 £182 cao
Answer: £182
Question 27
M1 original numbers found: total parts 7 + 2 + 1 = 10, unit value 450/10 = 45, so home = 315, away = 90, neutral = 45
M1 dep: 30 neutral seats split equally, so 15 seats added to home and 15 to away
M1 dep: new numbers found (home = 330, away = 105, neutral = 15) and simplified using HCF 15