Percentage increase, profit and discounts

Increasing and decreasing by a percentage with multipliers, percentage change, profit and loss, discounts, GST and finding the original price.

Multipliers

Example 1●

Increase $\$80$ by $15\%$, and decrease $\$250$ by $30\%$.

$80 \times 1.15 = \$92$

$250 \times 0.7 = \$175$

Percentage change

$$\%\ \text{change} = \frac{\text{change}}{\text{original}} \times 100\%$$

Example 2●●

A phone case costs a shop $\$40$ and sells for $\$52$. Find the percentage profit.

Profit $= \$12$

$\dfrac{12}{40} \times 100\% = 30\%$

Example 3●●●

After a $25\%$ discount, a jacket costs $\$60$. Find the original price.

$60$ is $75\%$ of the original: $0.75 \times P = 60$.

$P = 60 \div 0.75 = \$80$

Flashcards

Increase by 15%

× 1.15

Decrease by 30%

× 0.7

GST in a GST-inclusive price

Price ÷ 11

Practice

Increase $\$80$ by $15\%$.
Decrease $\$250$ by $30\%$.
Cost $\$40$, sold for $\$52$. Percentage profit?
After a $25\%$ discount a jacket costs $\$60$. Original price?
Find the sale price of an $\$85$ item with $20\%$ off.
A GST-inclusive price is $\$110$. How much GST is included?
A bike bought for $\$500$ is sold for $\$400$. Find the percentage loss.
A price rises by $10\%$ and then by another $10\%$. What single multiplier is this?