A price falls by 10\% to 45. Find the original. [3 marks]

SQA SQA National 5 2019-style practice: A house is bought for 180\,000 and appreciates by 4\% each year. Find its value after 3 years, to the nearest pound.

Appreciating by 4\% means multiplying by 1.04 each year (1 mark). After 3 years the value is 180000 × 1.04^3 (1 mark). Evaluate: 1.04^3 = 1.124864, so 180000 × 1.124864 = 202\,475 to the nearest pound (1 mark). Markers reward the multiplier 1.04, raising it to the power 3, and the rounded value.

SQA SQA National 5 2022-style practice: In a sale, the price of a coat is reduced by 20\% to 60. Calculate the original price.

After a 20\% reduction, 60 represents 80\% of the original (1 mark). So 80\% of the original is 60, meaning 1\% is 6080 = 0.75 (1 mark). The original (100\%) is 0.75 × 100 = 75 (1 mark). Markers reward recognising 60 as 80\%, scaling to 1\%, and the original price. Dividing 60 by 0.8 gives the same answer.

ScotlandMathsSyllabus dot point

How do you work with percentage increase and decrease, reverse percentages, and repeated percentage change such as compound interest and appreciation?

Calculating percentage increase and decrease, finding the original amount in reverse percentage problems, and using a multiplier for repeated percentage change including appreciation, depreciation and compound interest.

A focused answer to the SQA National 5 Mathematics percentages content, covering percentage increase and decrease using a multiplier, reverse percentage problems to find an original amount, and repeated percentage change such as compound interest, appreciation and depreciation.

Generated by Claude Opus 4.810 min answerUpdated 2026-06-14

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Jump to a section

What this dot point is asking
Percentage increase and decrease with a multiplier
Reverse percentages
Repeated percentage change
Examples in context
Try this

What this dot point is asking

The SQA wants you to calculate a percentage increase or decrease, solve reverse-percentage problems to find an original amount, and handle repeated percentage change such as compound interest, appreciation and depreciation using a multiplier.

Percentage increase and decrease with a multiplier

The quickest way to change an amount by a percentage is to multiply by a single number. To increase by $r\%$ , multiply by $1 + \dfrac{r}{100}$ ; to decrease, multiply by $1 - \dfrac{r}{100}$ .

Reverse percentages

A reverse-percentage problem gives you the amount after a change and asks for the original. The key is to recognise what percentage of the original the given amount represents, then scale back to $100\%$ .

A price rises by 20 percent to 90 pounds. Find the original price.

The key insight for a reverse percentage is to identify what percentage of the original the given amount represents, then scale back to $100\%$ .

Step 1: Identify what percentage of the original the new amount represents

A $20\%$ rise means the new price is $100\% + 20\% = 120\%$ of the original. So $\pounds 90$ represents $120\%$ of the original price.

Step 2: Scale back to find 100 percent

If $120\%$ corresponds to $\pounds 90$ , then $1\%$ is $\dfrac{90}{120} = \pounds 0.75$ . Multiply by $100$ to find the full original amount:

100\% = 0.75 \times 100 = \pounds 75

Final answer: The original price was $\pounds 75$ .

The common mistake here is to take $20\%$ off the new price; you must divide by the multiplier ( $1.20$ ), not subtract a percentage of the wrong amount.

Repeated percentage change

When a percentage change is applied again and again, each new amount is a percentage of the previous one, so you raise the multiplier to a power. This covers compound interest (money growing in a bank), appreciation (a rise in value) and depreciation (a fall in value).

The power equals the number of times the change is applied, which is usually the number of years. Compound growth and decline both use the same structure; only the multiplier differs, being above $1$ for growth and below $1$ for decline.

Examples in context

Percentages run through everyday finance. A savings account paying $3\%$ compound interest a year multiplies the balance by $1.03$ annually, so after $5$ years $\pounds 1000$ becomes $1000 \times 1.03^5 = \pounds 1159.27$ . Shops use reverse percentages when a sale price is shown but the original is wanted. Tax, tips and inflation are all percentage changes applied to a base amount.

Try this

Q1. Decrease $\pounds 80$ by $5\%$ . [2 marks]

Cue. $80 \times 0.95 = \pounds 76$ .

Q2. A price falls by $10\%$ to $\pounds 45$ . Find the original. [3 marks]

Cue. $45 \div 0.9 = \pounds 50$ .

Q3. $\pounds 2000$ earns $4\%$ compound interest for $3$ years. Find the total. [3 marks]

Cue. $2000 \times 1.04^3 = \pounds 2249.73$ .

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA National 5 20193 marksA house is bought for

\pounds 180\,000

and appreciates by

4\%

each year. Find its value after

3

years, to the nearest pound.

Show worked answer →

Appreciating by $4\%$ means multiplying by $1.04$ each year (1 mark). After $3$ years the value is $180000 \times 1.04^3$ (1 mark). Evaluate: $1.04^3 = 1.124864$ , so $180000 \times 1.124864 = \pounds 202\,475$ to the nearest pound (1 mark). Markers reward the multiplier $1.04$ , raising it to the power $3$ , and the rounded value.

SQA National 5 20223 marksIn a sale, the price of a coat is reduced by

20\%

\pounds 60

. Calculate the original price.

Show worked answer →

After a $20\%$ reduction, $\pounds 60$ represents $80\%$ of the original (1 mark). So $80\%$ of the original is $\pounds 60$ , meaning $1\%$ is $\dfrac{60}{80} = \pounds 0.75$ (1 mark). The original ( $100\%$ ) is $0.75 \times 100 = \pounds 75$ (1 mark). Markers reward recognising $\pounds 60$ as $80\%$ , scaling to $1\%$ , and the original price. Dividing $60$ by $0.8$ gives the same answer.

Related dot points

Sources & how we know this

SQA National 5 Mathematics Course Specification — SQA (2018)