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Year 8AC9M8N05

Percentage Increase, Decrease and Profit

Use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts.

One multiplier does the whole job. Learn to write it and every percentage question becomes a single calculation.

Method

The multiplier
+r%⇒×(1+r100)−r%⇒×(1−r100)+r\% \Rightarrow \times(1 + \tfrac{r}{100}) \qquad -r\% \Rightarrow \times(1 - \tfrac{r}{100})
One step instead of two.
Percentage change compares with the original
% change=changeoriginal×100\%\text{ change} = \frac{\text{change}}{\text{original}} \times 100
Always divide by what you started with.
Profit and loss use the cost price
Divide by what it cost, never by what it sold for.
Reversing a change means dividing
original=newmultiplier\text{original} = \frac{\text{new}}{\text{multiplier}}
Do not subtract the percentage back off.

Worked example

e.g. A jacket bought for $60 sells for $75. Find the percentage profit.\text{A jacket bought for } \$60 \text{ sells for } \$75. \text{ Find the percentage profit.}
  1. Find the profit in dollars.75−60=1575 - 60 = 15
  2. Write it as a fraction of the cost price.1560\frac{15}{60}
  3. Multiply by 100.1560×100=25\frac{15}{60} \times 100 = 25
  4. State it in context.a 25% profit\text{a } 25\% \text{ profit}
  5. Check with the multiplier.60×1,25=75✓60 \times 1{,}25 = 75 \quad\checkmark

Practice

Write the multiplier first, then calculate once.

1
Increase 80 by 15%\text{Increase } 80 \text{ by } 15\%
Answer80×1,15=9280 \times 1{,}15 = 92
2
Decrease 250 by 12%\text{Decrease } 250 \text{ by } 12\%
Answer250×0,88=220250 \times 0{,}88 = 220
3
Cost 40, sells 34. Percentage loss?\text{Cost } 40, \text{ sells } 34. \text{ Percentage loss?}
Answer15%15\%
4
A price after 20% off is $64. Find the original.\text{A price after } 20\% \text{ off is } \$64. \text{ Find the original.}
Answer64÷0,8=$8064 \div 0{,}8 = \$80
5
A price rises 25% then falls 20%. Net change?\text{A price rises } 25\% \text{ then falls } 20\%. \text{ Net change?}
Answer1,25×0,8=1no change1{,}25 \times 0{,}8 = 1 \quad \text{no change}
6
Why divide by the cost price for profit?\text{Why divide by the cost price for profit?}
AnswerProfit is measured against what you paid.\text{Profit is measured against what you paid.}
Next step
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