A bag contains 8 red counters and 12 blue counters. Write the ratio of red counters to blue counters in its simplest form.
(Total for Question 2 is 1 mark)
3
Complete the missing number: 3 : 5 = 12 : ___
(Total for Question 3 is 1 mark)
4
Which of these ratios is NOT equivalent to 3 : 4?
A) 6 : 8
B) 9 : 12
C) 12 : 15
D) 15 : 20
(Total for Question 4 is 1 mark)
5
Amy and Ben share 40 sweets in the ratio 3 : 5. Calculate how many sweets each person receives.
(Total for Question 5 is 2 marks)
6
There are 30 pupils in a class. The ratio of boys to girls is 2 : 3. Calculate the number of girls in the class.
(Total for Question 6 is 2 marks)
7
A fruit drink is made from cordial and water in the ratio 2 : 7. Calculate how much water is needed for 50 ml of cordial.
(Total for Question 7 is 2 marks)
8
The ratio of red marbles to blue marbles in a jar is 3 : 7. Calculate what percentage of the marbles in the jar are blue.
(Total for Question 8 is 2 marks)
9
A recipe for 4 people needs 300 g of flour, 150 g of sugar and 2 eggs. Rewrite the recipe for 10 people.
(a)Calculate the mass of flour needed for 10 people.(1)
(b)Calculate the mass of sugar needed for 10 people.(1)
(c)Calculate the number of eggs needed for 10 people.(1)
(Total for Question 9 is 3 marks)
10
9 identical notebooks cost £13.50. Calculate the cost of 5 of these notebooks.
(Total for Question 10 is 3 marks)
11
Shop A sells 6 pens for £2.40. Shop B sells 9 pens for £3.15. Work out which shop offers better value for money, showing your working.
(Total for Question 11 is 3 marks)
12
£72 is shared between Priya, Tom and Sara in the ratio 2 : 3 : 4.
(a)Calculate how much Sara receives.(2)
(b)Calculate how much more Sara receives than Priya.(1)
(Total for Question 12 is 3 marks)
13
A map has a scale of 1 : 25 000. Two towns are 6 cm apart on the map. Calculate the real distance between the towns, giving your answer in kilometres.
(Total for Question 13 is 3 marks)
14
1 km/h is equivalent to 5/18 m/s. Convert a speed of 90 km/h into m/s.
(Total for Question 14 is 2 marks)
15
In an animal shelter, the ratio of cats to dogs is 4 : 5.
(a)There are 20 dogs in the shelter. Calculate the number of cats.(2)
(b)8 of the cats are rehomed, and no dogs leave the shelter. Calculate the new ratio of cats to dogs, giving your answer in its simplest form.(2)
(Total for Question 15 is 4 marks)
16
It takes 4 builders working at the same constant rate 6 hours to build a wall. Calculate how long it would take 8 builders, working at the same rate, to build an identical wall.
(Total for Question 16 is 3 marks)
17
A car travels at a constant speed and covers 180 km in 2.5 hours. Calculate how far the car would travel in 4 hours at the same speed.
(Total for Question 17 is 3 marks)
18
In a swimming club, the ratio of boys to girls is 7 : 5. There are 18 more boys than girls. Calculate the total number of members in the club.
(Total for Question 18 is 3 marks)
19
Zara, Leo and Priya invest money in a business in the ratio 2 : 3 : 5 respectively. The business makes a profit of £600, which is shared in the same ratio as their investment. Calculate how much more profit Priya receives than Zara.
(Total for Question 19 is 3 marks)
20
A photograph measuring 10 cm by 15 cm is enlarged proportionally so that its new width is 25 cm. Calculate the new height of the enlarged photograph.
(Total for Question 20 is 3 marks)
21
Two numbers are in the ratio 4 : 7. Their sum is 121. Calculate the difference between the two numbers.
(Total for Question 21 is 3 marks)
22
A metal alloy is made from copper and tin in the ratio 5 : 3. A jeweller has 45 g of copper.
(a)Calculate how much tin must be added to the copper to make the alloy.(2)
(b)Calculate the total mass of alloy produced.(1)
(Total for Question 22 is 3 marks)
23
In a school, the ratio of Year 7 pupils to Year 8 pupils is 5 : 4. The ratio of Year 8 pupils to Year 9 pupils is 3 : 2. Calculate the ratio of Year 7 to Year 8 to Year 9 pupils, giving your answer in its simplest form.
(Total for Question 23 is 3 marks)
24
A sum of money is divided between Liam and Noah in the ratio 5 : 3. Liam receives £45 more than Noah. Calculate the total sum of money divided between them.
(Total for Question 24 is 4 marks)
25
A school has 288 pupils. The ratio of pupils who walk, cycle or travel by car to school is 5 : 1 : 3. The number of pupils who cycle is expected to increase by 50%, while the total number of pupils remains 288 and the ratio of walk to car (among the remaining pupils) stays the same as before. Calculate the new ratio of walk to cycle to car, giving your answer in its simplest form.
(Total for Question 25 is 4 marks)
Mark scheme · EP.M6 Ratio and Proportion
Question 1
B1 3 : 4 oe cao
Answer: 3 : 4
Question 2
B1 2 : 3 oe cao
Answer: 2 : 3
Question 3
B1 20 cao
Answer: 20
Question 4
B1 C (12:15) cao
Answer: C) 12 : 15
Question 5
M1 total parts found (3 + 5 = 8) and 40/8 = 5 used, or equivalent method
A1 Amy = 15 and Ben = 25 cao
Answer: Amy = 15 sweets, Ben = 25 sweets
Question 6
M1 total parts found (2 + 3 = 5) and 30/5 = 6 used, or equivalent method
A1 18 cao
Answer: 18
Question 7
M1 scale factor found: 50/2 = 25, or equivalent method
A1 175 ml cao
Answer: 175 ml
Question 8
M1 total parts found (3 + 7 = 10) and 7/10 used, or equivalent method
A1 70% cao
Answer: 70%
Question 9
(a) B1 750 g cao
(a) Answer: 750 g
(b) B1 375 g cao
(b) Answer: 375 g
(c) B1 5 eggs cao
(c) Answer: 5 eggs
Question 10
M1 cost of 1 notebook found: 13.50/9 = 1.50
M1 dep: their 1.50 x 5
A1 £7.50 cao
Answer: £7.50
Question 11
M1 price per pen at Shop A found: 2.40/6 = 0.40
M1 price per pen at Shop B found: 3.15/9 = 0.35
A1 Shop B offers better value (cao, since £0.35 per pen is less than £0.40 per pen)
Answer: Shop B (£0.35 per pen versus £0.40 per pen at Shop A)
Question 12
(a) M1 total parts found (2 + 3 + 4 = 9) and 72/9 = 8 used, or equivalent method
(a) A1 £32 cao
(a) Answer: £32
(b) B1 £16 (ft from part a: Priya = 2 x their unit value, then Sara - Priya)
(b) Answer: £16
Question 13
M1 real distance found in cm: 6 x 25 000 = 150 000
M1 dep: converts their 150 000 cm to metres then kilometres (150 000 / 100 = 1500 m, then / 1000)
A1 1.5 km cao
Answer: 1.5 km
Question 14
M1 90 x 5/18 oe set up
A1 25 m/s cao
Answer: 25 m/s
Question 15
(a) M1 unit value found: 20/5 = 4, or equivalent method
(a) A1 16 cao
(a) Answer: 16
(b) M1 new number of cats found (ft from part a): 16 - 8 = 8
(b) A1 2 : 5 oe cao
(b) Answer: 2 : 5
Question 16
M1 total worker-hours found: 4 x 6 = 24
M1 dep: their 24 / 8
A1 3 hours cao
Answer: 3 hours
Question 17
M1 speed found: 180/2.5 = 72 km/h
M1 dep: their 72 x 4
A1 288 km cao
Answer: 288 km
Question 18
M1 difference in parts found (7 - 5 = 2) and unit value found (18/2 = 9)
M1 dep: total parts found (7 + 5 = 12) and their 9 x 12
A1 108 cao
Answer: 108
Question 19
M1 total parts found (2 + 3 + 5 = 10) and unit value found: 600/10 = 60
M1 dep: Priya's share and Zara's share found (5 x 60 = 300, 2 x 60 = 120)
A1 £180 cao
Answer: £180
Question 20
M1 scale factor found: 25/10 = 2.5
M1 dep: their 2.5 x 15
A1 37.5 cm cao
Answer: 37.5 cm
Question 21
M1 total parts found (4 + 7 = 11) and unit value found: 121/11 = 11
M1 dep: the two numbers found (4 x 11 = 44, 7 x 11 = 77)
A1 33 cao
Answer: 33
Question 22
(a) M1 unit value found: 45/5 = 9
(a) A1 27 g cao
(a) Answer: 27 g
(b) B1 72 g (ft from part a: 45 + their tin mass)
(b) Answer: 72 g
Question 23
M1 finds a common value for Year 8 in both ratios (e.g. scales 5:4 to 15:12 and 3:2 to 12:8, using the LCM of 4 and 3, which is 12)
M1 dep: combines to give 15 : 12 : 8
A1 15 : 12 : 8 cao (already in simplest form, HCF = 1)
Answer: 15 : 12 : 8
Question 24
M1 difference in parts found: 5 - 3 = 2
M1 dep: unit value found: 45/2 = 22.50
M1 dep: total parts found (5 + 3 = 8) and their 22.50 x 8
A1 £180 cao
Answer: £180
Question 25
M1 original numbers found: total parts 5 + 1 + 3 = 9, unit value 288/9 = 32, so walk = 160, cycle = 32, car = 96
M1 dep: new cycle number found: 32 x 1.5 = 48
M1 dep: remaining pupils (288 - 48 = 240) split in the ratio 5:3 (unit value 240/8 = 30), giving walk = 150 and car = 90