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Level 7Grade 7skill: profit_loss· 8 min read

Profit and Loss: Cost, Selling Price, Percent

In short: Profit = SP - CP and profit percent is always measured against the cost price: Profit% = (Profit ÷ CP) × 100. To find SP, multiply CP by (1 + p/100); to find CP from SP, divide by (1 + p/100). The number-one trap is dividing by the selling price instead of the cost price.

The four quantities, and the one rule that ties them together

Every profit-and-loss question is built from just two numbers: the cost price (CP) — what the seller paid — and the selling price (SP) — what a customer paid. Everything else is derived from those two.

If SP is bigger, the difference is profit. If CP is bigger, the difference is a loss. The part that trips up otherwise careful students is the percent. A profit percent is never just "the gap in dollars" — it is that gap measured against the cost price, then scaled to 100. Profit% = (Profit ÷ CP) × 100. The denominator is CP. Always CP. Not SP, not the average, not whichever number is handy.

Once you trust that rule, the reverse questions become mechanical. If a jacket sells at 25% profit, its SP is CP × 1.25. Turn that around and CP = SP ÷ 1.25 — you divide the selling price by the growth factor rather than subtracting a percent of it.

  1. Write down what you know: CP, SP, and whether a profit% or loss% is given.
  2. Profit (dollars) = SP - CP. If the answer is negative, it is a loss of that many dollars.
  3. Profit% = (Profit ÷ CP) × 100. Loss% = (Loss ÷ CP) × 100. The base is CP every single time.
  4. To go forward: SP = CP × (1 + p/100) for profit, or CP × (1 - p/100) for loss.
  5. To go backward: CP = SP ÷ (1 + p/100) for profit, or SP ÷ (1 - p/100) for loss.
  6. If the question is per-item (per apple, per metre), find CP and SP for the SAME quantity before dividing.

Why the base is always the cost price Why it works

Find profit%
Divide the dollar profit by CP, then multiply by 100.

$100 profit on a CP of $400 is 100/400×100 = 25% — never 100/500, which would give a tempting-but-wrong 20%.

Find SP
SP = CP × (1 + p/100).

CP $400 at 25% profit → 400 × 1.25 = $500.

Find CP from SP
CP = SP ÷ (1 + p/100) — divide, don't subtract a percent of SP.

SP $575 at 15% profit → 575 ÷ 1.15 = $500.

Here is the one insight worth carrying out of this article: profit and loss percents are quoted on the cost price because the cost is what the seller risked. The selling price already contains the profit inside it, so measuring against SP uses a base that already includes that profit — which always understates the true return. When a question hands you the selling price and a percent, resist subtracting a slice of that selling price — divide instead.

Worked examples

Leo buys a basketball bat for $400 and sells it for $500. Find his profit and profit percent. = Profit $100, which is a 25% profit.
  1. Profit = SP - CP = 500 - 400 = $100.
  2. Profit% = (Profit ÷ CP) × 100 = (100 ÷ 400) × 100.
  3. 100 ÷ 400 = 0.25, and 0.25 × 100 = 25.
A shirt is sold for $500 at a profit of $100. What is the profit percent? = 25% (the base is the $400 cost price).
  1. The dollar profit is given as $100, and SP = $500.
  2. Work out CP first: CP = SP - Profit = 500 - 100 = $400.
  3. Profit% = (100 ÷ 400) × 100 = 25%. Dividing by 500 instead would give 20% — that is the trap.
A fruit seller buys 15 mangoes for $300 and sells them at $24 each. Find the profit percent. = 20% profit.
  1. Cost of one mango = 300 ÷ 15 = $20.
  2. Selling price of one mango = $24, so profit per mango = 24 - 20 = $4.
  3. Profit% = (4 ÷ 20) × 100 = 20%. (Check with totals: SP = 15 × 24 = $360, profit = 360 - 300 = $60, and 60/300 = 20%.)
A watch was sold for $575 at a 15% profit. Find the cost price. = $500. (Subtracting 15% of $575 gives $488.75, which is wrong — never take the percent off the selling price.)
  1. SP = CP × (1 + 15/100) = CP × 1.15.
  2. So CP = 575 ÷ 1.15 = $500.
  3. Check: 15% of 500 = 75, and 500 + 75 = $575. Correct.
A trader buys 20 notebooks at $25 each, but water damage forces him to sell the whole lot for $450. Is it a profit or a loss, and what percent? = A 10% loss.
  1. Total CP = 20 × 25 = $500. Total SP = $450.
  2. SP - CP = 450 - 500 = -$50, so it is a loss of $50.
  3. Loss% = (50 ÷ 500) × 100 = 10%.

Traps that cost careful students marks

Dividing the profit by the selling price

✗ 20%

With a $100 profit on a $400 cost sold for $500, this student computes 100 ÷ 500 × 100 = 20%. The selling price already includes the profit, so it is the wrong base.

Fix: Profit% is always Profit ÷ CP. Here that is 100 ÷ 400 × 100 = 25%.

base_confusion

Stopping at the dollar profit

✗ $100

Asked for the selling price of a $400 item at 25% profit, this student finds the profit (25% of 400 = $100) and writes $100 — but that is the profit, not the price.

Fix: Add the profit back to the cost: SP = 400 + 100 = $500.

partial_computation

Misplacing the decimal in the percent

✗ $1000

To find 25% of $400 you multiply by 0.25. Slipping the decimal one place turns 0.25 into 2.5, giving 2.5 × 400 = $1000 of "profit" on a $400 item — impossible.

Fix: 25% = 0.25, so 0.25 × 400 = $100. Sanity-check: a profit can't dwarf the cost like that.

decimal_point_shift

Using the percent number as dollars

✗ $25

For a 25% profit on $400, this student writes the profit as $25 — pasting the number 25 straight in as if the percent sign were not there.

Fix: Convert first: 25% of 400 = 0.25 × 400 = $100, not $25.

percent_as_whole

Reporting a loss as a profit

✗ a $50 profit (10% profit)

Buying 20 notebooks at $25 (CP $500) and selling for $450 gives SP - CP = -$50. This student drops the minus sign and calls it a $50 profit.

Fix: A negative result means a loss. It is a $50 loss, so a 50/500 × 100 = 10% loss.

sign_error

Adding the percent instead of multiplying

✗ $425

To raise $400 by 25%, this student adds the number 25 to 400 to get $425, mixing up "add 25%" with "add 25."

Fix: Multiply by the growth factor: 400 × 1.25 = $500. Adding a raw 25 has no meaning here.

wrong_operation

Practice: profit, loss and percent

Work through a set of grade-7 profit-and-loss problems. Watch for the questions that hand you the selling price — decide whether to divide by the growth factor or subtract, and always measure your percent against the cost price.

Keep building

First, make sure of

Frequently asked questions

Is profit percent calculated on the cost price or the selling price?

Always on the cost price. Profit% = (Profit ÷ Cost Price) × 100. A $100 profit on a $400 cost is 25%, not 100/500 = 20%. The selling price already contains the profit, so using it as the base understates the real return.

How do I find the cost price when I only know the selling price and the profit percent?

Divide, don't subtract. If SP = $575 at 15% profit, then CP = 575 ÷ 1.15 = $500. Taking 15% off the $575 (giving $488.75) is wrong because the 15% was measured against the cost, not the selling price.

What's the difference between profit and profit percent?

Profit is a dollar amount: SP - CP. Profit percent scales that amount against the cost and multiplies by 100. So a $100 profit on $400 is a 25% profit — same situation, two different questions, and you must read which one is being asked.

How do I handle per-item problems, like buying 15 mangoes for $300?

Bring both prices to the same quantity first. Cost per mango = 300 ÷ 15 = $20; if each sells for $24, profit per mango is $4, so profit% = 4/20 × 100 = 20%. You can also compare totals (SP $360 vs CP $300) — either route gives the same percent.

What tells me a transaction is a loss?

When the cost price is greater than the selling price, so SP - CP comes out negative. The size of that negative number is the loss in dollars, and Loss% = (Loss ÷ CP) × 100. Don't drop the minus sign and call it a profit.