8.7Profit, Loss and Discount

Businesses use percentages to express profitability and savings. There are two separate chains to keep track of:

Cost price → Selling price: Determines profit or loss.
Marked price → Selling price: Determined by discount.

All three follow the same shape, and the only thing that changes is what you divide by.

	The amount	As a percentage	Divide by
Profit	selling price $-$ cost price	$\dfrac{\text{profit}}{\text{cost price}} \times 100\%$	COST price
Loss	cost price $-$ selling price	$\dfrac{\text{loss}}{\text{cost price}} \times 100\%$	COST price
Discount	marked price $-$ selling price	$\dfrac{\text{discount}}{\text{marked price}} \times 100\%$	MARKED price

That last column is the whole trap: profit and loss are measured against what the seller PAID, a discount against what the shop ASKED.

Profit percentage

A mobile phone accessories shop buys a Bluetooth earphone set for $\displaystyle \$45$ and sells it for $\displaystyle \$63$ . Find the profit percentage.

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\displaystyle \text{Profit}

\displaystyle = \$63 - \$45

\displaystyle = \$18

\displaystyle \text{Profit percentage}

\displaystyle = \dfrac{18}{45} \times 100\%

\displaystyle = 40\%

Discount and selling price

A hawker stall sells fishball noodles at a marked price of $\displaystyle \$6$ . During a senior citizen promotion, a $\displaystyle 15\%$ discount is given. Find the selling price.

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\displaystyle \text{Discount}

\displaystyle = 15\% \text{ of } \$6

\displaystyle = \dfrac{15}{100} \times 6.00

\displaystyle = \$0.90

\displaystyle \text{Selling price}

\displaystyle = \$6 - \$0.90

\displaystyle = \$5.10

Now you try

The marked price of an item is $\$300$ . A discount of $10\%$ is given. Find the sale price.

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Discount

= 10\%

\$300

\displaystyle = \frac{10}{100} \times 300 = \$30

\displaystyle \text{Sale price}

\displaystyle = \$300 - \$30

\displaystyle = \$270

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