Financial Accounting · Incomplete records

Mark-ups and Margins in Incomplete Records Questions

Updated 11 October 2026 · Fact-checked

Mark-up is gross profit as a percentage of cost of sales. Margin is gross profit as a percentage of sales. To solve a question, write sales, cost of sales and gross profit as a ratio, such as 100 : 60 : 40 for a 40% margin, then scale from the one figure you know.

Understand Mark-ups and Margins

In incomplete records questions, some figures are missing. You may not know sales, purchases or closing inventory. Often you are told how the business prices its goods. That pricing gives you a link between sales, cost of sales and gross profit, and the link lets you find the missing figure.

There are two ways to state that link. Mark-up is the profit added on top of cost. Margin is the profit as a share of the selling price. The profit is the same. Only the base differs. Mark-up uses cost of sales as 100%. Margin uses sales as 100%.

Example: goods cost $80 and sell for $100. Gross profit is $20. Mark-up is 20 ÷ 80 = 25%. Margin is 20 ÷ 100 = 20%. Same sale, two different percentages. For the same goods, margin is always lower than mark-up, as long as profit is positive.

The safest way to use either is a three-line table: Sales, Cost of sales, Gross profit. Put 100 against the base figure, work out the other two, and then scale. Once you have the missing figure for sales or cost of sales, you can use it in a trading account or ledger reconstruction, for example to find missing closing inventory or purchases.

Key formulas to remember

Mark-up: Mark-up % = Gross profit ÷ Cost of sales × 100; The base is cost of sales. Cost of sales = 100%.
Margin: Margin % = Gross profit ÷ Sales × 100; The base is sales. Sales = 100%.
Basic link: Sales = Cost of sales + Gross profit; This holds in every question. Use it to fill the gaps.
Sales from cost with mark-up: Sales = Cost of sales × (1 + mark-up %); A 25% mark-up means sales = cost × 1.25.
Cost from sales with margin: Cost of sales = Sales × (1 − margin %); A 20% margin means cost = sales × 0.80.
Margin to mark-up: Mark-up % = Margin % ÷ (100% − Margin %); A 20% margin gives 20 ÷ 80 = 25% mark-up.
Mark-up to margin: Margin % = Mark-up % ÷ (100% + Mark-up %); A 25% mark-up gives 25 ÷ 125 = 20% margin.
Cost of sales: Cost of sales = Opening inventory + Purchases − Closing inventory; Use this once you know cost of sales, to find a missing purchases or inventory figure.

How to solve Mark-ups and Margins questions

Use the same method for any question where sales, cost of sales or gross profit is missing.

1Read the question and note whether the percentage is a mark-up or a margin. Look for the words 'on cost' or 'on sales' too.
2Draw a three-line table: Sales, Cost of sales, Gross profit.
3Put 100 against the base: cost of sales for mark-up, sales for margin.
4Fill the other lines. For a 25% mark-up: cost 100, profit 25, sales 125. For a 20% margin: sales 100, profit 20, cost 80.
5Find which actual figure you know, such as sales or cost of sales. Scale the table to match it.
6Read off the missing figure, such as sales or gross profit.
7If needed, put the result into the cost of sales calculation (opening inventory + purchases − closing inventory) to find the final missing item.
8Check: sales minus cost of sales must equal gross profit, and the percentage must reproduce your base.

Quickest way: Ratio shortcut

When to use it: Use it when the question gives one known figure and one percentage, and you need sales, cost or gross profit quickly.

Turn the percentage into a ratio. Mark-up 25% on cost gives cost : profit : sales = 4 : 1 : 5. Margin 20% gives sales : profit : cost = 5 : 1 : 4.
Divide the known figure by its ratio part to get one unit.
Multiply the unit by the ratio part you need.
Do a quick check that sales is the largest figure and equals cost plus profit.

Common mistakes in Mark-ups and Margins

Applying a mark-up percentage to sales.
Students see 'profit is 25%' and take it off sales without checking the base.
Fix: If it is mark-up, the base is cost. Put 100 against cost of sales first.
Treating margin and mark-up as the same number.
Both are gross profit percentages and look alike.
Fix: Remember the base: mark-up on cost, margin on sales. Convert only with the formulas.
Multiplying cost by (1 − margin) to get sales, or dividing wrongly.
Students memorise formulas without thinking about what the numbers mean.
Fix: Use the table. With a 20% margin, cost is 80% of sales, so sales = cost ÷ 0.80.
Converting by simply adding or subtracting percentage points.
It seems logical that 25% mark-up equals 25% margin less something.
Fix: Use margin ÷ (100 − margin) or mark-up ÷ (100 + mark-up).
Using sales or purchases where cost of sales is needed.
Inventory movements are forgotten.
Fix: Cost of sales = opening inventory + purchases − closing inventory. Adjust for goods taken for own use or stolen when told.
Ignoring that only some sales are at the stated margin.
Students rush and apply the percentage to every figure.
Fix: Read for exceptions such as goods sold at a different price and handle those separately.

Worked examples

Example 1

A trader has no sales records. Opening inventory was $12,000, purchases were $68,000 and closing inventory was $10,000. The trader sells goods at a mark-up of 40% on cost. Calculate sales and gross profit.

Show the solution

Cost of sales = 12,000 + 68,000 − 10,000 = $70,000.
Mark-up is on cost, so cost of sales = 100% and sales = 140%.
Sales = 70,000 × 1.40 = $98,000.
Gross profit = 98,000 − 70,000 = $28,000.
Check: 28,000 ÷ 70,000 = 40%.

Answer: Sales are $98,000 and gross profit is $28,000.

Example 2

A business earns a gross profit margin of 25% on sales. Sales for the year were $240,000. Opening inventory was $18,000 and closing inventory was $22,000. Calculate purchases.

Show the solution

Margin is on sales, so sales = 100% and cost of sales = 75%.
Cost of sales = 240,000 × 0.75 = $180,000.
Cost of sales = opening inventory + purchases − closing inventory.
180,000 = 18,000 + purchases − 22,000.
Purchases = 180,000 − 18,000 + 22,000 = $184,000.
Check: 18,000 + 184,000 − 22,000 = 180,000.

Answer: Purchases were $184,000.

Exam tips

Underline whether the question says mark-up or margin before you do anything else.
Draw the three-line table every time. It takes ten seconds and avoids base errors.
In number entry questions, check the units and rounding instruction before typing your answer.
In multiple choice, the wrong options are often what you get by using the wrong base. If your answer matches one, check twice.
Section B incomplete records questions often need the cost of sales formula after the mark-up step, so leave time for that second step.

Practice questions from Incomplete records

Mark-ups and Margins in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Mark-ups and Margins: frequently asked questions

What is the difference between mark-up and margin?

Mark-up is gross profit divided by cost of sales. Margin is gross profit divided by sales. The profit is the same, but the base is different, so the margin percentage is always lower than the mark-up percentage when profit is positive.

How do I convert gross profit margin to mark-up?

Divide the margin by 100% minus the margin. For example, a 20% margin gives 20 ÷ 80 = 25% mark-up. To go the other way, divide the mark-up by 100% plus the mark-up.

How do I calculate sales from mark-up in incomplete records?

First find cost of sales from opening inventory, purchases and closing inventory. Then multiply cost of sales by 1 plus the mark-up. A 30% mark-up means sales are cost of sales × 1.30.

Do I need to memorise both conversion formulas?

It helps, but the table method gives the same result. A 25% mark-up is cost 100, profit 25, sales 125, so the margin is 25 ÷ 125 = 20%.