A recipe uses flour and sugar in the ratio 4:1. For a larger batch using the same ratio, how many parts of sugar are needed for 20 parts of flour?
(1)
3
A map has a scale of 1 cm to 5 km. Work out the real distance represented by 9 cm on the map.
(1)
4
Work out 30% of 90 pounds.
(1)
5
Two amounts are shared in the ratio 3:5. The total is 40. Work out the smaller share.
(1)
6
A recipe is scaled up by a factor of 3. If the original amount of butter is 60 g, work out the new amount.
(1)
7
A cyclist travels 15 km in 30 minutes at a steady speed. Work out the speed in km/h.
(1)
8
Write 3/4 as a percentage.
(1)
9
A charity raises money split between two projects in the ratio 5:3. The total raised is 96 pounds. Work out how much the project with the larger share receives.
(2)
10
A model car is built at a scale of 1:24. The model is 18 cm long. Work out the length of the real car, in metres.
(2)
11
A metal alloy is made from copper and tin in the ratio 7:1. Work out how many kg of copper are in 48 kg of the alloy.
(2)
12
A jacket priced at 80 pounds is reduced by 35% in a sale. Work out the sale price.
(2)
13
A crew of workers paints a fence at a steady combined rate of 12 metres per hour. Work out how many metres they paint in 2 hours 30 minutes.
(2)
14
A fruit drink is made from juice and water in the ratio 2:9. Work out how many litres of water are needed for 4 litres of juice.
(2)
15
A charity shop prices donated books and DVDs in the ratio 5:2. If 210 items are donated in total in that ratio, work out how many are DVDs.
(3)
16
A drink is diluted with concentrate and water in the ratio 1:9. A jug needs to hold 650 ml of the diluted drink. Work out how much concentrate is needed, in ml.
(3)
17
A toy shop applies a 25% discount to a game, then adds a 4% handling fee to the discounted price. The original price is 60 pounds. Work out the final price, to the nearest penny.
(3)
18
A van uses fuel at a rate of 8.5 litres per 100 km. Work out how many litres are needed for a 340 km journey.
(3)
19
A youth club has members in the ratio of juniors to seniors of 5:3. After 4 juniors leave and 2 seniors join, the ratio becomes 3:2. Work out how many members were in the club originally.
(4)
20
A bakery mixes flour and water in the ratio 11:5. It needs at least 48 kg of mixture. Work out the least whole number of kilograms of flour required.
(4)
Mark scheme · KS3.M-R11D Proportional Reasoning Problem Set: Fluency and Exam Drill
Question 1
B1 3/5 cao
Answer: 3/5
Question 2
B1 5 parts cao
Answer: 5 parts
Question 3
B1 45 km cao
Answer: 45 km
Question 4
B1 27 (pounds) cao
Answer: 27 pounds
Question 5
B1 15 cao
Answer: 15
Question 6
B1 180 g cao
Answer: 180 g
Question 7
B1 30 km/h cao
Answer: 30 km/h
Question 8
B1 75% cao
Answer: 75%
Question 9
M1 total parts 5+3 = 8, one part = 96/8 = 12
A1 60 (pounds) cao
Answer: 60 pounds
Question 10
M1 method: 18*24 = 432 cm
A1 4.32 m cao
Answer: 4.32 m
Question 11
M1 total parts 7+1 = 8, one part = 48/8 = 6
A1 42 kg cao
Answer: 42 kg
Question 12
M1 method: 80*0.65 or find 35% and subtract
A1 52 (pounds) cao
Answer: 52 pounds
Question 13
M1 convert 2 hours 30 minutes to 2.5 hours
A1 30 m cao
Answer: 30 m
Question 14
M1 find the scale factor: 4/2 = 2
A1 18 litres cao
Answer: 18 litres
Question 15
M1 total parts 5+2 = 7, one part = 210/7 = 30
M1 DVDs = 2*30
A1 60 DVDs cao
Answer: 60 DVDs
Question 16
M1 total parts 1+9 = 10, one part = 650/10 = 65
M1 concentrate is 1 part so 65
A1 65 ml cao
Answer: 65 ml
Question 17
M1 apply the discount: 60*0.75 = 45
M1 apply the fee: 45*1.04
A1 46.80 (pounds) cao
Answer: 46.80 pounds
Question 18
M1 method: 8.5/100 * 340 or (340/100)*8.5
M1 compute 340*8.5 = 2890 then divide by 100
A1 28.9 litres cao
Answer: 28.9 litres
Question 19
M1 set up: let multiplier be k, juniors = 5k, seniors = 3k; after change juniors = 5k-4, seniors = 3k+2
M1 equation (5k-4)/(3k+2) = 3/2 or 2(5k-4) = 3(3k+2)
M1 solve: 10k-8 = 9k+6 gives k = 14
A1 total members originally = 5k+3k = 8k = 8*14 = 112 cao
Answer: 112
Question 20
M1 flour:water = 11:5 so water = 5/11 of flour; total = flour + 5/11 flour = 16/11 flour, and 16/11 flour ≥ 48
M1 so flour ≥ 48*11/16 = 33
M1 check flour = 33 gives total 48 kg exactly, meeting the requirement; flour = 32 gives total 46.545 kg, which fails