A jacket that normally costs 80 pounds is reduced by 25%. Work out the sale price.
(1)
3
Find 5% of 240.
(1)
4
Increase 150 by 18%. Give your answer to the nearest whole number.
(2)
5
Write down the multiplier to decrease an amount by 30%.
(2)
6
A school dinner costs 2.40 pounds. Each year the price increases by 5%. Work out the cost after 2 years, correct to the nearest penny.
(3)
7
A printer cartridge is reduced by 20% in January and then by a further 10% in February. The original price was 45 pounds. Work out the price after the two reductions, giving your answer to the nearest 10 pence.
(3)
8
A coat is on sale for 84 pounds after a 30% reduction. Work out the original price of the coat.
(3)
9
An item costs 48 pounds and is later 54 pounds. Work out the percentage change, stating whether it is an increase or a decrease. Give your answer to one decimal place.
(2)
10
A phone price is increased by 15% and then decreased by 10%. If the original price was 200 pounds, find the final price. Explain briefly why this final price is not the same as increasing by 5% overall.
(3)
11
Sam buys a bicycle for 150 pounds and sells it to a friend making a 12% profit. The friend then sells the bicycle to another person at a 15% loss on the price they paid. Work out the final selling price to the third person. Give your answer to the nearest penny.
(4)
12
Write down the multiplier to increase an amount by 250%.
(1)
13
A town's population falls by 6% each year. The current population is 24 000. Work out the population after 3 years, giving your answer to the nearest whole number.
(3)
14
Express an increase of 40% as a multiplier and as a fractional multiplier.
(2)
15
Explain why increasing a number by 20% and then by 30% is not the same as increasing it by 50%. Give a short numerical example to support your explanation.
(2)
16
A table price including VAT is 240 pounds. The VAT rate is 20% added to the original price. Work out the price before VAT was added.
(3)
17
A small shop had sales of 12 500 pounds last year. Sales rose by 3% in the first year and by 4% in the second year. Work out the sales after the two years, correct to the nearest pound.
(3)
18
Stretch question. After two successive percentage changes the final price of an item is 198 pounds. First it was increased by p% and then decreased by 10%, where p is 20. Work out the original price before the two changes. Show your steps.
(4)
Mark scheme · KS3.M-R7 Percentage Change and Multipliers
Question 1
B1 36 cao
Answer: 36
Question 2
B1 60 pounds cao
Answer: 60 pounds
Question 3
B1 12 cao
Answer: 12
Question 4
M1 use of 150 x 1.18 or calculation of 18% = 27 and addition
A1 177 cao
Answer: 177
Question 5
M1 correct reasoning: 100% - 30% = 70% or 0.70
A1 0.7 or 0.70 cao
Answer: 0.7
Question 6
M1 use of multiplier 1.05 twice or equivalent method
M1 correct intermediate value 2.40 x 1.05 = 2.52 or evidence of both steps
A1 2.65 (pounds) cao
Answer: 2.65
Question 7
M1 use of multiplier 0.8 then 0.9 or combined multiplier 0.72
M1 calculation 45 x 0.72 = 32.4 or equivalent two-step shown
A1 32.4 pounds (or 32.40) cao
Answer: 32.4
Question 8
M1 recognition that 84 = 70% of original or use 84 / 0.7
M1 division to find original price
A1 120 pounds cao
Answer: 120 pounds
Question 9
M1 correct method: (54 - 48)/48 x 100 or equivalent
A1 12.5% increase cao
Answer: 12.5% increase
Question 10
M1 use of multipliers 1.15 and 0.9 or calculation steps shown leading to 200 x 1.15 x 0.9
M1 correct final price calculation 200 x 1.035 = 207 or equivalent
A1 207 pounds and explanation that successive percentage changes multiply not add, so 1.15 x 0.9 = 1.035 not 1.05
Answer: 207 pounds
Question 11
M1 apply 12% profit: 150 x 1.12 = 168.00 or evidence
M1 apply 15% loss: 168 x 0.85 or equivalent
M1 correct multiplication 168 x 0.85 = 142.8
A1 142.80 pounds cao
Answer: 142.80 pounds
Question 12
B1 3.5 or 3.50 cao (100% + 250% = 350% = 3.5)
Answer: 3.5
Question 13
M1 use of multiplier 0.94 three times or combined multiplier 0.943
M1 correct intermediate calculation e.g. 24000 x 0.94 = 22560 then further steps
A1 19934 (population) cao
Answer: 19934
Question 14
M1 recognition that 100% + 40% = 140% giving 1.4
A1 1.4 and 7/5 cao
Answer: 1.4 and 7/5
Question 15
M1 correct statement that multipliers multiply not add (1.2 x 1.3 = 1.56 not 1.5)
A1 example such as starting with 100 gives 100 x1.2 x1.3 = 156 not 150 cao
Answer: Because multipliers multiply: 1.2 x 1.3 = 1.56, so 100 -> 156 not 150
Question 16
M1 recognition that 240 = 120% of original or use 240 / 1.2
M1 division to find original price
A1 200 pounds cao
Answer: 200 pounds
Question 17
M1 use of multipliers 1.03 then 1.04 or combined 1.03 x 1.04
M1 intermediate calculation 12500 x 1.03 = 12875 or similar
A1 13390 pounds cao
Answer: 13390
Question 18
M1 use of multiplier for increase 1 + p/100 = 1.20 and decrease multiplier 0.9 to form equation original x 1.20 x 0.9 = 198
M1 correct combination 1.20 x 0.9 = 1.08 or equivalent