CP Formula — How to Find Cost Price, Examples

TL;DR
The CP formula recovers the cost price of an item from its selling price and a profit or loss: CP=SP−profit, CP=SP+loss, and from a percentage, CP=100/(100 + profit%) × SP or 100/(100 - loss%) × SP. This article derives all four forms, defines every term, and works six examples plus the percentage mistakes that flip answers.

What Is the CP Formula?

Cost price (CP) is the price at which an item is bought; selling price (SP) is the price at which it is sold. Profit and loss are the difference between them, and the CP formula rearranges those definitions to solve for the cost.

There are four forms, depending on what the problem gives you:

CP=SP−profit(\text{CP} = \text{SP} - \text{profit})
CP=SP+loss(\text{CP} = \text{SP} + \text{loss})

(\text{CP} = \frac{100}{100 + \text{profit%}} \times \text{SP})
(\text{CP} = \frac{100}{100 - \text{loss%}} \times \text{SP})

Symbol	Meaning
CP	Cost price — what the seller paid
SP	Selling price — what the buyer paid
profit	SP−CP, when SP is higher
loss	CP−SP, when CP is higher
profit% / loss%	The gain or shortfall as a percentage of CP

Because every percentage here is a share measured against a base, the topic leans on the same comparison logic as the ratio formula. The single most important fact about this formula: profit% and loss% are always calculated on the cost price, not the selling price.

How Do You Find Cost Price When Profit Percentage Is Given?

This is the most-asked version of the question, and the percentage form is where readers get stuck. Start from the definition. If profit is a percentage of CP, then:

(\text{SP} = \text{CP} + \text{profit%} \times \text{CP} = \text{CP}\left(1 + \frac{\text{profit%}}{100}\right) = \text{CP} \times \frac{100 + \text{profit%}}{100}.)

Rearranging for CP:
(\text{CP} = \frac{100}{100 + \text{profit%}} \times \text{SP}.)
The loss case is identical with a minus sign — a loss makes SP smaller than CP, so the denominator is 100 - loss%:
(\text{CP} = \frac{100}{100 - \text{loss%}} \times \text{SP}.)

Examples of the CP Formula

Example 1

A toy is sold for 340$ at a profit of 60$. Find the cost price.
CP=SP−profit=340−60=280.(\text{CP} = \text{SP} - \text{profit} = 340 - 60 = 280.)
Final answer: $$280$.

Example 2

An article is sold for $$230$ at a $25%$ profit. Find the cost price.
Wrong attempt. A student takes 25% of the selling price — 0.25×230=57.5 — and subtracts it: 230−57.5=172.5. Check it by working forward: a cost of 172.5 at 25% profit gives 172.5×1.25=215.6, not 230. The profit percentage was taken on the wrong base — it belongs to the cost price, which is the unknown.
Correct. Use the percentage form, with profit% on CP:
CP=100/(100+25)×230=100/125×230=184.(\text{CP} = \frac{100}{100 + 25} \times 230 = \frac{100}{125} \times 230 = 184.)
Final answer: $$184$. Check: $184 × 1.25 = 230$. ✓

Example 3

An item is sold for 250$ at a loss of 20$. Find the cost price.
A loss means cost was higher than selling price:
CP=SP+loss=250+20=270.(\text{CP} = \text{SP} + \text{loss} = 250 + 20 = 270.)
Final answer: $$270$.

Example 4

A chair is sold for $$900$ at a $6%$ loss. Find the cost price.
CP=100/(100−6)×900=100/94×900≈957.45.(\text{CP} = \frac{100}{100 - 6} \times 900 = \frac{100}{94} \times 900 \approx 957.45.)
Final answer: $$957.45$ (to the nearest cent).

Example 5

A shopkeeper sells a watch for $$1{,}200$, earning a $20%$ profit. What did the watch cost?
CP=100/120×1200=1000.(\text{CP} = \frac{100}{120} \times 1200 = 1000.)
Final answer: $$1{,}000$. Check: $1000 × 1.20 = 1200$. ✓

Example 6

A phone bought at cost price was sold for $$540$ after a $10%$ loss. The seller then wants to know the original cost and the loss amount.
Cost price first:
CP=100/(100−10)×540=100/90×540=600.(\text{CP} = \frac{100}{100 - 10} \times 540 = \frac{100}{90} \times 540 = 600.)
Loss amount =CP−SP=600−540=60= \text{CP} - \text{SP} = 600 - 540 = 60.
Final answer: Cost price 600$, loss 60$.

Why Cost Price Matters — The Number Behind Every Markup

Cost price was singled out as the base for percentages because it is the only fixed reference in a trade — the selling price moves, but what you paid does not.

Retail pricing. Every markup, discount, and sale tag is computed relative to cost price; a shop that prices off the selling price loses track of its actual margin.
Break-even analysis. A business finds the point where total cost equals total revenue by working from cost price — sell above it and you profit, below it and you lose.
Accounting and inventory. Goods are recorded at cost price on the balance sheet; the profit only appears when they sell.
Personal trades. Reselling a phone, a bike, or a concert ticket is the same arithmetic — the gain or loss is always measured against what you paid.

The destination, a couple of chapters on, is compound growth: once profit% on cost price is comfortable, the same percentage-on-a-base idea becomes compound interest, where each period's base is last period's total.

Where Cost-Price Problems Go Wrong

Mistake 1: Taking the percentage on the selling price

Where it slips in: Any "find CP given SP and profit%/loss%" problem.
Don't do this: Compute profit% of the selling price and subtract it. Profit% is defined on cost price, which is the unknown — not on SP.
The correct way: Use CP = 100/(100 + profit%) × SP.

Mistake 2: Using the wrong sign for profit versus loss

Where it slips in: Switching between profit and loss problems.
Don't do this: Use 100 + loss% in the denominator, or CP=SP−loss.
The correct way: Profit makes CP smaller than SP, so subtract profit / use 100 + profit%. Loss makes CP larger than SP, so add loss / use 100 - loss%.

Mistake 3: Confusing cost price with marked price

Where it slips in: Problems that also mention a marked (list) price and a discount.
Don't do this: Treat the marked price as the cost price. The marked price is what the item is listed at before discount; the cost price is what the seller paid.

Conclusion

The CP formula finds cost price from selling price: CP=SP−profit and CP=SP+loss.
From a percentage, CP=100/(100 + profit%) × SP for profit and 100/(100 - loss%) × SP for loss.
Profit% and loss% are always calculated on the cost price, never on the selling price.
The most common mistake is taking the percentage on the selling price instead of CP.

Try These Three Before Moving On

An item sells for 480$ at a 80$ profit. Find the cost price.
A bag sells for $$540$ at a $10%$ profit. Find the cost price.
A book sells for $$144$ at a $20%$ loss. Find the cost price.

Answer to Question 1: $$400$. Solve Questions 2 and 3 with the percentage forms; if your forward-check does not return the selling price, return to Mistake 1.