Worked examples
Mark-up and margin: worked examples
Two worked examples using mark-up and margin to rebuild missing figures, as in incomplete-records questions. All figures are our own.
Example 1
A trader marks goods up by 25% on cost. Sales for the year were RM50,000. Find the cost of sales and gross profit.
| Sales | RM 50,000 |
| Cost of sales (50,000 ÷ 1.25) | RM 40,000 |
| Gross profit | RM 10,000 |
Try it yourself: what is the gross profit as a margin? (10,000 ÷ 50,000 = 20%.)
Example 2
A business has a gross margin of 30% and cost of sales of RM35,000. Find sales and gross profit.
| Cost of sales | RM 35,000 |
| Gross profit (30/70 × 35,000) | RM 15,000 |
| Sales | RM 50,000 |
Try it yourself: express this as a mark-up on cost. (15,000 ÷ 35,000 = about 43%.)
Method and where the marks are
Mark-up and margin questions test whether you can move between cost, profit and selling price. The topic rests on knowing which figure each ratio is based on. Mark-up is gross profit as a fraction or percentage of cost price.
Margin is gross profit as a fraction or percentage of selling price. Both describe the same gross profit. They divide it by different figures.
First identify which one you have been given. Using cost as the base when you should use selling price, or the reverse, gives an answer that looks plausible but earns nothing.
Build a simple three-line structure for every question: cost of sales, gross profit and sales. Cost plus gross profit equals sales. If you are given a mark-up, treat cost as the whole, or the base of 100.
Suppose cost is RM200 and the mark-up is 25%. Gross profit is 25% of RM200, which is RM50, and sales are RM250. If you are given a margin, treat sales as the whole.
With sales of RM250 and a margin of 20%, gross profit is 20% of RM250, which is RM50, and cost of sales is RM200. Mark which line is your 100 base. It keeps your reasoning visible and protects the method marks if you slip on arithmetic.
Examiners often give one ratio and expect you to use the other, so learn to convert. A mark-up of 1/4 on cost becomes a margin of 1/5 on sales. For every 4 parts of cost there is 1 part of profit, and so 5 parts of selling price.
Going the other way, a margin of 1/5 becomes a mark-up of 1/4. Be able to derive this from "cost plus profit equals sales" and do not just memorise it.
The main use of these ratios is to find a missing figure when records are incomplete or stock has been lost. If you know sales and the margin, you can find gross profit and then cost of sales. If you know cost of sales and the mark-up, you can find gross profit and then sales.
Put every figure you can find into the trading account layout and let the balancing figure reveal the unknown. This can give a missing closing inventory, such as stock destroyed in a fire.
Marks are mostly lost on three points. The first is applying a mark-up percentage to the selling price, or a margin percentage to the cost. Always ask what the whole is before you multiply.
The second is confusing gross profit with net profit. These ratios work on gross profit only, before expenses. The third is careless conversion, such as turning a 1/4 mark-up into a 1/4 margin.
A quick check catches most errors. Margin as a percentage is always smaller than the matching mark-up, because it is divided by the larger figure. If your margin is larger than your mark-up, you have made an error.
Show your base clearly and keep cost, gross profit and sales on separate labelled lines. Carry the figures into a proper trading account. Do not round midway if the question uses exact amounts, because early rounding can throw the balancing figure off.
If you are given sales and a mark-up and asked for cost, you can divide sales by 1 plus the mark-up. For a 25% mark-up, divide by 1.25.
If you often mix up the two bases, we can help. One of our teachers can work through a set of mark-up and margin questions with you until choosing the base is automatic. Book a trial class
These are our own worked solutions and commentary, not the board's mark scheme. For official papers, see the exam boards page.
Practise mark-up and margin with a teacher
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