A tray holds 14 lemon flapjacks and 21 ginger flapjacks. Write the ratio of lemon flapjacks to ginger flapjacks in its simplest form.
(Total for Question 2 is 1 mark)
3
Complete the missing number: 5 : 8 = 35 : ___
(Total for Question 3 is 1 mark)
4
Which of these ratios is NOT equivalent to 4 : 7?
A) 8 : 14
B) 12 : 21
C) 16 : 27
D) 20 : 35
(Total for Question 4 is 1 mark)
5
A box of biscuits contains plain biscuits and chocolate biscuits in the ratio 5 : 3. Calculate what percentage of the biscuits are chocolate biscuits.
(Total for Question 5 is 2 marks)
6
Priya and Sam share 72 conkers in the ratio 5 : 4. Calculate how many conkers Sam receives.
(Total for Question 6 is 2 marks)
7
There are 45 pupils in a school choir. The ratio of sopranos to altos is 7 : 2. Calculate how many altos are in the choir.
(Total for Question 7 is 2 marks)
8
£40 is shared between Alex and Priya in the ratio 3 : 5. How much does Alex receive?
A) £15
B) £20
C) £25
D) £30
(Total for Question 8 is 1 mark)
9
A flapjack recipe for 6 people uses 240 g of butter, 180 g of golden syrup, 2 eggs and 320 g of oats. The recipe is scaled up for 9 people.
(a)Calculate the mass of butter needed for 9 people.(1)
(b)Calculate the mass of golden syrup needed for 9 people.(1)
(c)Calculate the number of eggs needed for 9 people.(1)
(d)Calculate the mass of oats needed for 9 people.(1)
(Total for Question 9 is 4 marks)
10
7 identical notepads cost £16.10 in total. Calculate the cost of 3 of these notepads.
(Total for Question 10 is 2 marks)
11
Shop E sells a 750 g bag of pasta for £1.35. Shop F sells a 1.2 kg bag of the same pasta for £2.04. Work out which shop offers better value for money, showing your working.
(Total for Question 11 is 3 marks)
12
A charity raises £360, which is shared between three local projects, a food bank, a youth club and a park refurbishment, in the ratio 4 : 3 : 2. Calculate how much more money the food bank receives than the park refurbishment project.
(Total for Question 12 is 3 marks)
13
A map has a scale of 1 : 50 000. Two church towers are 7.4 cm apart on the map. Calculate the real distance between them, giving your answer in kilometres.
(Total for Question 13 is 3 marks)
14
y is directly proportional to x. When x = 6, y = 15. Calculate the value of y when x = 20.
(Total for Question 14 is 2 marks)
15
It takes 5 identical pipes, running at the same constant rate, 8 hours to fill a reservoir. Calculate how long it would take 4 of these pipes, running at the same rate, to fill the same reservoir.
(Total for Question 15 is 3 marks)
16
A car uses fuel at a constant rate. It uses 6 litres of fuel to travel 84 km. How far can it travel on 10 litres of fuel at the same rate?
A) 126 km
B) 140 km
C) 150 km
D) 168 km
(Total for Question 16 is 1 mark)
17
In an allotment association, the ratio of members who grow vegetables to members who grow flowers is 5 : 3. There are 12 more vegetable growers than flower growers. Calculate the total number of members in the association.
(Total for Question 17 is 3 marks)
18
A photograph measuring 8 cm by 14 cm is enlarged proportionally so that its new width is 20 cm. Calculate the new height of the photograph.
(Total for Question 18 is 3 marks)
19
Elliot, Farah and Deshawn invest money in a business in the ratio 3 : 4 : 5 respectively. The business makes a profit of £720, which is shared in the same ratio as their investment. Calculate how much profit Farah receives.
(Total for Question 19 is 3 marks)
20
Two numbers are in the ratio 5 : 9. Their difference is 32. Calculate the sum of the two numbers.
(Total for Question 20 is 3 marks)
21
A sum of money is divided between Grace and Tobias in the ratio 7 : 4. Grace receives £54 more than Tobias. Calculate the total sum of money divided between them.
(Total for Question 21 is 4 marks)
22
A stationery shop sells notebooks in three pack sizes: a pack of 4 for £3.00, a pack of 6 for £4.50, and a pack of 9 for £7.20. Calculate the price per notebook for each pack size, and state which pack size (or sizes) offer the best value for money.
(Total for Question 22 is 3 marks)
23
In a school, the ratio of Year 9 pupils to Year 10 pupils is 6 : 5. The ratio of Year 10 pupils to Year 11 pupils is 4 : 3. Calculate the ratio of Year 9 to Year 10 to Year 11 pupils, giving your answer in its simplest form.
(Total for Question 23 is 3 marks)
24
It takes 8 painters, working at the same constant rate, 15 days to redecorate a hotel corridor. The hotel manager wants the job finished in 6 days. Calculate how many painters, working at the same rate, are needed to finish the job in 6 days.
(Total for Question 24 is 3 marks)
25
A festival has 600 tickets allocated to three ticket types, early bird, standard and VIP, in the ratio 8 : 5 : 2. Before the festival, 40 VIP tickets are reallocated equally between early bird and standard, while the total number of tickets stays at 600. Calculate the new ratio of early bird to standard to VIP tickets, giving your answer in its simplest form.
(Total for Question 25 is 4 marks)
26
A recipe for 5 people uses 400 g of rice. Bakari has 900 g of rice and wants to use exactly 90% 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 90% of Bakari's rice.
(Total for Question 26 is 4 marks)
Mark scheme · EP.M50 Ratio and Proportion: Practice Set 3
Question 1
B1 A (3 : 4) cao
Answer: A) 3 : 4
Question 2
B1 2 : 3 oe cao
Answer: 2 : 3
Question 3
B1 56 cao
Answer: 56
Question 4
B1 C (16:27) cao
Answer: C) 16 : 27
Question 5
M1 total parts found (5 + 3 = 8) and fraction 3/8 set up, or equivalent method
A1 37.5% oe cao
Answer: 37.5%
Question 6
M1 total parts found (5 + 4 = 9) and unit value found: 72/9 = 8
A1 32 cao
Answer: 32
Question 7
M1 total parts found (7 + 2 = 9) and unit value found: 45/9 = 5
A1 10 cao
Answer: 10
Question 8
B1 A (£15) cao
Answer: A) £15
Question 9
(a) B1 360 g cao
(a) Answer: 360 g
(b) B1 270 g cao
(b) Answer: 270 g
(c) B1 3 eggs cao
(c) Answer: 3 eggs
(d) B1 480 g cao
(d) Answer: 480 g
Question 10
M1 unit cost found: 16.10/7 = 2.30
A1 £6.90 cao
Answer: £6.90
Question 11
M1 price per 100 g at Shop E found: (1.35/750) x 100 = 0.18
M1 price per 100 g at Shop F found: (2.04/1200) x 100 = 0.17
A1 Shop F offers better value cao (£0.17 per 100 g versus £0.18 per 100 g at Shop E)
Answer: Shop F (£0.17 per 100 g versus £0.18 per 100 g at Shop E)
Question 12
M1 total parts found (4 + 3 + 2 = 9) and unit value found: 360/9 = 40
M1 dep: food bank share and park refurbishment share found (4 x 40 = 160, 2 x 40 = 80)
A1 £80 cao
Answer: £80
Question 13
M1 real distance found in cm: 7.4 x 50 000 = 370 000
M1 dep: converts their 370 000 cm to metres then kilometres (370 000/100 = 3700 m, then /1000)
A1 3.7 km cao
Answer: 3.7 km
Question 14
M1 constant of proportionality found: k = 15/6 = 2.5, or equivalent scale factor method
A1 50 cao
Answer: 50
Question 15
M1 total 'pipe-hours' found: 5 x 8 = 40
M1 dep: their 40/4
A1 10 hours cao
Answer: 10 hours
Question 16
B1 B (140 km) cao
Answer: B) 140 km
Question 17
M1 difference in parts found (5 - 3 = 2) and unit value found (12/2 = 6)
M1 dep: total parts found (5 + 3 = 8) and their 6 x 8
A1 48 cao
Answer: 48
Question 18
M1 scale factor found: 20/8 = 2.5
M1 dep: their 2.5 x 14
A1 35 cm cao
Answer: 35 cm
Question 19
M1 total parts found (3 + 4 + 5 = 12) and unit value found: 720/12 = 60
M1 dep: their 4 x 60
A1 £240 cao
Answer: £240
Question 20
M1 difference in parts found (9 - 5 = 4) and unit value found: 32/4 = 8
M1 dep: the two numbers found (5 x 8 = 40, 9 x 8 = 72)
A1 112 cao
Answer: 112
Question 21
M1 difference in parts found: 7 - 4 = 3
M1 dep: unit value found: 54/3 = 18
M1 dep: total parts found (7 + 4 = 11) and their 18 x 11
A1 £198 cao
Answer: £198
Question 22
M1 price per notebook found for the pack of 4 and the pack of 6: 3.00/4 = 0.75, 4.50/6 = 0.75
M1 dep: price per notebook found for the pack of 9: 7.20/9 = 0.80, and all three compared
A1 the pack of 4 and the pack of 6 are joint best value at £0.75 each, cheaper than the pack of 9 at £0.80 cao
Answer: Packs of 4 and 6 are joint best value (£0.75 per notebook each); the pack of 9 is worse value (£0.80 per notebook)
Question 23
M1 finds a common value for Year 10 in both ratios (e.g. scales 6:5 to 24:20 and 4:3 to 20:15, using the LCM of 5 and 4, which is 20)
M1 dep: combines to give 24 : 20 : 15
A1 24 : 20 : 15 cao (already in simplest form, HCF = 1)
Answer: 24 : 20 : 15
Question 24
M1 total 'painter-days' found: 8 x 15 = 120
M1 dep: their 120/6
A1 20 painters cao
Answer: 20 painters
Question 25
M1 original numbers found: total parts 8 + 5 + 2 = 15, unit value 600/15 = 40, so early bird = 320, standard = 200, VIP = 80
M1 dep: 40 VIP tickets split equally, so 20 tickets added to early bird and 20 to standard
M1 dep: new numbers found (early bird = 340, standard = 220, VIP = 40) and simplified using HCF 20
A1 17 : 11 : 2 cao
Answer: 17 : 11 : 2
Question 26
M1 90% of 900 g found: 810 g
M1 dep: rice needed per person found: 400/5 = 80 g
M1 dep: their 810/80 = 10.125
A1 10 (people) cao, rounded down since only whole servings are possible