Selling Price Formula - Definition, Steps, Examples

Key Points

• The selling price formula is $\text{SP} = \text{CP} + \text{Profit}$, and becomes $\text{SP} = \text{CP} - \text{Loss}$ when the sale loses money.

• With a profit percentage the formula is $\text{SP} = \text{CP}\left(1 + \frac{p}{100}\right)$, where the percentage is always taken on the cost price.

• Coming from a listed price instead, the selling price is $\text{SP} = \text{MP} - \text{Discount}$, with the discount percentage taken on the marked price.

• The two routes use different bases, so a profit percentage and a discount percentage can never be added or compared directly.

• Recovering a cost price from a selling price means dividing by $1 + \frac{p}{100}$, not subtracting the percentage.

What Is the Selling Price Formula?

The selling price formula gives the amount a customer actually pays. Starting from cost:

$$\text{SP} = \text{CP} + \text{Profit} = \text{CP}\left(1 + \frac{p}{100}\right)$$

Starting from a listed price instead:

$$\text{SP} = \text{MP} - \text{Discount} = \text{MP}\left(1 - \frac{d}{100}\right)$$

Both give the same selling price for the same transaction. Which one to use depends on whether the known quantity is the cost or the listed price.

Why the Base Decides the Answer

Every percentage in commercial arithmetic is a percentage of something, and selling price problems contain two candidates. Profit is measured on the cost price; discount is measured on the marked price.

Using the wrong one does not produce a small error, it produces a different quantity. A 25 per cent profit on a cost of 80 gives 100, while a 25 per cent discount from a marked price of 80 gives 60.

So the first step in any selling price question is identifying which base the percentage belongs to. The words cost, bought and purchased point to the cost price; marked, listed and labelled point to the marked price.

Variable Key

Examples of the Selling Price Formula

Example 1

An article costs 400 and is sold at a 25 per cent profit. Find the selling price.

$$\text{SP} = 400\left(1 + \frac{25}{100}\right) = 400 \times 1.25 = 500$$

Final answer: 500

Example 2

An article costs 400 and is sold at a 25 per cent profit. Find the selling price by taking 25 per cent of the selling price.

It is tempting to read "25 per cent profit" as a share of the money received, so that the profit is a quarter of the selling price. Try it: if profit is a quarter of $\text{SP}$, then $\text{CP}$ is three quarters of it, giving

$$\text{SP} = \frac{400}{0.75} \approx 533.33$$

That answer belongs to a different question. A 25 per cent profit means 25 per cent of what the seller paid, so the base is the cost price, not the selling price.

$$\text{SP} = 400 \times 1.25 = 500$$

Final answer: 500. The 533.33 figure would be correct for a 25 per cent margin on the selling price, which is a separate measure.

Example 3

An item marked 1,200 is sold at a 15 per cent discount. Find the selling price.

$$\text{SP} = 1200 \times 0.85 = 1020$$

Final answer: 1,020

Example 4

An article costing 250 is sold at a 12 per cent loss. Find the selling price.

A loss reverses the sign in the bracket:

$$\text{SP} = 250\left(1 - \frac{12}{100}\right) = 250 \times 0.88 = 220$$

Final answer: 220

Example 5

An article sells for 690 at a 15 per cent profit. Find the cost price.

The selling price is 115 per cent of the cost, so divide:

$$\text{CP} = \frac{690}{1.15} = 600$$

Final answer: 600

Subtracting 15 per cent of 690 would give 586.50, which is wrong because that takes the percentage on the selling price rather than the cost price.

Don't Confuse These Four Prices and Rates

Profit percentage and margin are the pair most often confused, because both compare the same money gain. A 25 per cent profit on cost is a 20 per cent margin on the selling price, so the two numbers describe one transaction differently.

Common Errors When Working With Selling Price

Mistake 1: Taking the profit percentage on the selling price

Where it slips in: Profit arrives with the sale, so the selling price feels like the natural reference.

Don't do this: Treat a 25 per cent profit as a quarter of the selling price.

The correct way: Profit percentage uses the cost price as its base, so $\text{SP} = \text{CP} \times 1.25$. If a question genuinely wants a share of revenue, it will say margin.

Students who underline the base word in the question, cost or marked, before writing anything down stop choosing the wrong denominator. The error is almost never arithmetic; it is reading.

Mistake 2: Subtracting a percentage to recover the cost price

Where it slips in: Undoing a 15 per cent profit feels like removing 15 per cent.

Don't do this: $690 - 15$ of $690 = 586.50$.

The correct way: Divide by 1.15 to get 600. Subtracting takes the percentage on the wrong quantity, and the gap grows as the percentage grows.

Mistake 3: Adding a profit percentage and a discount percentage

Where it slips in: Both appear in the same problem, so they look like they belong on one scale.

Don't do this: Treat a 20 per cent markup followed by a 20 per cent discount as breaking even.

The correct way: Apply them in sequence to their own bases. On a cost of 100, marking up 20 per cent gives 120, and a 20 per cent discount on 120 gives 96, so the seller makes a loss.

The Short Version

• The selling price formula is $\text{SP} = \text{CP}(1 + \frac{p}{100})$ from cost, or $\text{MP}(1 - \frac{d}{100})$ from a listed price.

• Profit and loss percentages sit on the cost price, discounts sit on the marked price, and margin sits on the selling price.

• Identifying the base is the whole problem, and choosing wrongly returns a different quantity rather than a near miss.

• Recovering a cost price means dividing by the growth factor, never subtracting the percentage.

• To work through profit and loss with a teacher, explore an 8th grade math tutor or math tuition.

Practice These Three Before Moving On

Find the selling price for a cost of 750 at a 16 per cent profit. Then recover the cost price of an item sold at 924 after a 10 per cent loss, and check it by reapplying the loss.

Want a live Bhanzu trainer to walk through more profit and loss problems? Book a free demo class.

Read More

• Discount Formula

• Profit Formula

• Profit and Loss Formula

• Percentage Increase Formula

• Fractions, Decimals and Percentages