Percentages: O-Level / IGCSE Maths (0580)

Syllabus C1.13, E1.13 · Strand 1 Number

Questions: 4
Total marks: 26
Tier mix: 1 Core · 3 Extended

Percentages are a way of expressing a quantity as a number of parts per hundred, so $37\%$ simply means $\tfrac{37}{100}=0.37$ . This topic (syllabus C1.13 / E1.13) collects together the everyday calculations that rely on this idea: finding a percentage of an amount, increasing or decreasing a quantity by a given percentage, and expressing one quantity as a percentage of another. The starting point is converting freely between percentages, fractions and decimals, since most methods are quickest once the percentage is written as a decimal multiplier.

The central technique is the multiplier. To find $15\%$ of a value you multiply by $0.15$ ; to increase by $15\%$ you multiply by $1.15$ , and to decrease by $15\%$ you multiply by $0.85$ . Writing one quantity as a percentage of another uses $\dfrac{\text{part}}{\text{whole}}\times 100\%$ , which also handles percentage change via $\dfrac{\text{change}}{\text{original}}\times 100\%$ . Reverse percentages undo a change: if a price after a $15\%$ rise is known, the original is recovered by dividing by the multiplier, $\text{original}=\dfrac{\text{new value}}{1.15}$ ; a common pitfall is to subtract a percentage of the final amount instead. Repeated change, such as compound interest, applies the same multiplier several times, giving $A=P(1+r)^n$ for a rate $r$ per period over $n$ periods (with $1-r$ for repeated decrease or depreciation).

The exam-style problems below are original, written to match this syllabus objective, and each is followed by a full worked solution so you can compare your method step by step.

Question 1

Structured Core 6 marks

An electronics shop sells cameras, headphones and printers.

(a) A camera is priced at $240. A customer pays a deposit of $30\%$ of this price. Work out the deposit. [2]

(b) The shop buys a set of headphones for $48. To find the selling price, it increases this amount by $25\%$ . Work out the selling price. [2]

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Question 2

Structured Extended 8 marks

Brightline Electronics changes the prices of its products in several different ways. All prices already include any taxes.

(a) In a sale, the price of a tablet is reduced by $15\%$ . The sale price of the tablet is $612.

Calculate the original price of the tablet before the reduction. [2]

(b) The price of a games console is increased by $18\%$ . After this increase, the games console costs $1,121.

Work out the price of the games console before the increase. [3]

(c) The price of a laptop is first increased by $25\%$ . In a later sale, this higher price is then reduced by $12\%$ . After both of these changes, the laptop costs $1,419.

Calculate the original price of the laptop before either change was made. [3]

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Question 3

Multiple choice Extended 3 marks

Mariam invests $2,400 in a savings account that pays compound interest at a rate of $4.5\%$ per year. She makes no further deposits or withdrawals. Calculate the total amount in the account at the end of 3 years.

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Question 4

Structured Extended 9 marks

A furniture shop sells desks, chairs and shelving units.

(a) After a price rise of 15 per cent, a desk is now priced at $29.90. Work out the price of the desk before the rise. [2]

(b) A designer office chair is bought for $24000. Its value falls by 12 per cent each year. Work out the value of the chair after 3 years. Give your answer correct to the nearest dollar. [3]

(c) Meera invests $3500 in an account paying 4 per cent per year compound interest. Work out the total interest earned after 5 years. Give your answer correct to 2 decimal places. [4]

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