Edexcel GCSE Maths (1MA1), Higher tier · Ratio, proportion and rates of change
Practise Percentages and reverse percentages. 3 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy4 marks
(a) Decrease £105 by 5%.[2]
(b) Work out 15% of £260.[2]
Show the answer and mark scheme
(a)Answer: £99.75
M1 for 5% of £105 = £5.25 or \(105 \times 0.95\)
A1 for £99.75 cao
Worked solution: 5% of £105 = £5.25, so the answer is \(105 - 5.25 = 99.75\) pounds.
(b)Answer: £39
M1 for a correct method, e.g. 10% = £26 and 5% = £13, or \(0.15 \times 260\)
A1 for £39 cao
Worked solution: 10% = £26, 5% = £13. So 15% of £260 = £26 + £13 = £39.
Question 2Medium3 marks
In a sale, all prices are reduced by 20%. A jacket costs £36 in the sale. Tom says, 'The price before the sale was \(36 \times 1.2\) = £43.20.'
(a) Explain Tom's mistake.[1]
(b) Work out the price of the jacket before the sale.[2]
Show the answer and mark scheme
(a)Answer: The 20% was taken off the original price, not the sale price. £36 is 80% of the original price, so he should divide by 0.8.
C1 for explaining that £36 is 80% of the original price (the 20% is of the original price, not of £36)
Worked solution: Adding 20% of £36 is not the same as undoing a 20% reduction of the original price: 20% of the original price is more than 20% of £36.
(b)Answer: £45
M1 for \(36 \div 0.8\) or \(36 \div 80 \times 100\)
A1 for £45
Worked solution: 80% of the price is £36, so 1% is \(36 \div 80 = 0.45\) and 100% is £45.
Question 3Hard4 marks
In a sale, a shop reduces the normal price of a jacket by 25%. The sale price of the jacket is £60. When the shop sells the jacket at the sale price, it makes a profit of 50% on the cost price. Work out the percentage profit the shop makes when it sells the jacket at the normal price.[4]
Show the answer and mark scheme
Answer: 100%
P1 for the normal price, \(60 \div 0.75 = 80\)
P1 for the cost price, \(60 \div 1.5 = 40\)
P1 for \(\frac{80 - 40}{40} \times 100\) oe
A1 for 100% cao
Worked solution: Normal price \(= 60 \div 0.75 = 80\) pounds. Cost price \(= 60 \div 1.5 = 40\) pounds. Profit at the normal price \(= 80 - 40 = 40\), and \(\frac{40}{40} \times 100 = 100\)%.