Practice Maths

Percentage Increase and Decrease

Key Ideas

Key Terms

percentage increase
an increase of a given percentage above the original amount; new amount = original × (1 + rate).
percentage decrease
a reduction of a given percentage below the original amount; new amount = original × (1 − rate).
multiplier
the single decimal used to apply a percentage change in one step; e.g. +20% → 1.20; −15% → 0.85.
percentage change
the amount of change expressed as a percentage of the original: % change = (change ÷ original) × 100.

The multiplier method

A 25% increase → new = 125% of original → multiply by 1.25.
A 30% decrease → new = 70% of original → multiply by 0.70.

Hot Tip The multiplier method is fast and efficient. Increase by r% = multiply by (1 + r/100). Decrease by r% = multiply by (1 − r/100).

Worked Example

Question: A TV costs $850. It is increased in price by 12%. Find the new price.

Method — Multiplier.
Increase by 12% → multiply by 1.12.
New price = $850 × 1.12 = $952

Check — 12% of $850 = 0.12 × 850 = $102.
$850 + $102 = $952 ✓

The Multiplier Method for Increase and Decrease

The fastest way to apply a percentage increase or decrease is to use a multiplier — a single decimal you multiply the original amount by to get the new amount in one step.

Percentage increase: New = Original × (1 + rate/100)
e.g. Increase $200 by 20%: multiplier = 1 + 0.20 = 1.20. New = $200 × 1.20 = $240

Percentage decrease: New = Original × (1 − rate/100)
e.g. Decrease $200 by 15%: multiplier = 1 − 0.15 = 0.85. New = $200 × 0.85 = $170

Why does this work? A 20% increase means the new amount is 100% + 20% = 120% of the original = 1.20 times the original.

Calculating Percentage Change

If a value changes and you want to find what percentage it changed by, use:

% change = (change ÷ original) × 100

Where "change" = new value − old value (positive for increase, negative for decrease).

Example: A jacket cost $80 last season and now costs $96. What is the percentage increase?
Change = $96 − $80 = $16
% change = (16 ÷ 80) × 100 = 0.20 × 100 = 20% increase

Example: A footy team's crowd dropped from 25 000 to 20 000. % decrease = (5 000 ÷ 25 000) × 100 = 20% decrease.

Reverse Percentage — Finding the Original Amount

Sometimes you know the new amount and the percentage change, and you need the original. Divide the new amount by the multiplier.

Example: After a 25% price increase, a concert ticket costs $75. What was the original price?
Multiplier = 1.25
Original = $75 ÷ 1.25 = $60

Example: A laptop is on sale for $850 after a 15% discount. Original price?
Multiplier = 0.85
Original = $850 ÷ 0.85 = $1 000

Check: 15% of $1 000 = $150. $1 000 − $150 = $850. ✓

Real-Life Contexts

Percentage increase and decrease appear constantly in everyday life. Prices go up due to inflation. Sports stats track whether a team's score improved. Wages increase each year. Sales reduce prices. Understanding these calculations helps you evaluate whether a deal is really good or whether a statistic is actually significant.

Example: Your electricity bill was $180 last quarter. It increased by 8%. New bill = $180 × 1.08 = $194.40. The increase cost you $14.40 extra per quarter.

Example: A running personal best improved from 12 minutes to 10.5 minutes. % improvement = (1.5 ÷ 12) × 100 = 12.5% faster.

Key tip: Always divide by the original amount when calculating percentage change — never by the new amount. If you use the new amount as the denominator, your answer will be wrong. The original is your starting point; the change is measured relative to it.

Mastery Practice

  1. Find the new amount after each percentage increase. Fluency

    1. Increase 200 by 10%
    2. Increase $80 by 25%
    3. Increase 150 kg by 20%
    4. Increase $360 by 15%
    5. Increase 500 m by 8%
    6. Increase 75 by 40%
    7. Increase $1200 by 5%
    8. Increase 640 by 12.5%

  2. Find the new amount after each percentage decrease. Fluency

    1. Decrease 300 by 10%
    2. Decrease $240 by 25%
    3. Decrease 180 km by 30%
    4. Decrease $450 by 20%
    5. Decrease 800 mL by 5%
    6. Decrease 96 by 12.5%
    7. Decrease $2500 by 8%
    8. Decrease 160 by 35%

  3. Calculate the percentage change for each situation. State whether it is an increase or decrease. Understanding

    1. Original: 50, New: 65
    2. Original: 120, New: 90
    3. Original: $40, New: $46
    4. Original: 80 kg, New: 68 kg
    5. Original: $350, New: $385
    6. Original: 250, New: 175

  4. Find the original amount using the unitary method or reverse calculation. Understanding

    1. After a 20% increase, a price is $120. What was the original price?
    2. After a 10% decrease, a value is 72. What was the original?
    3. After a 25% increase, the number is 250. What was the original?
    4. After a 15% decrease, a salary is $2550. What was the original salary?

  5. Apply percentage increase and decrease to real situations. Problem Solving

    1. A shop owner buys goods for $480 and sells them with a 35% mark-up. What is the selling price?
    2. A car was originally priced at $28 000. After one year its value decreases by 18%. What is it worth after one year?
    3. A town’s population was 15 000 in 2020. By 2025 it had grown by 12%. What is the population in 2025?
    4. Emma scored 56 on a test last month and 70 this month. Calculate the percentage increase in her score.
    5. A jacket normally costs $240. It is reduced by 30%. The next week it is reduced by a further 20% off the sale price. What is the final price? Is this the same as a 50% reduction on the original?

  6. Find the new amount after each change. Fluency

    1. Increase $4500 by 6%
    2. Decrease 960 by 37.5%
    3. Increase 72 kg by 16⅔%
    4. Decrease $3200 by 12.5%
    5. Increase 0.8 km by 25%
    6. Decrease 144 by 33⅓%

  7. Write the multiplier for each percentage change. Understanding

    State the single multiplier you would use:

    1. Increase by 7%
    2. Decrease by 4%
    3. Increase by 100%
    4. Decrease by 100%
    5. Increase by 0.5%
    6. Decrease by 33⅓%
    7. Decrease by 2.5%
    8. Increase by 250%

  8. Find the percentage change. State if it is an increase or decrease. Understanding

    1. Original: 400, New: 460
    2. Original: $75, New: $60
    3. Original: 1200, New: 900
    4. Original: $0.80, New: $1.00
    5. Original: 48 kg, New: 52 kg
    6. Original: 360, New: 270

  9. Find the original value. Understanding

    1. After a 30% increase, the new value is 390. What was the original?
    2. After a 40% decrease, the value is 54. What was the original?
    3. A price including 10% GST is $242. What was the pre-GST price?
    4. A population grew by 8% to reach 16 200. What was the original population?
    5. After a 5% pay rise, an employee earns $630 per week. What was the previous weekly wage?

  10. Extended percentage change problems. Problem Solving

    1. A house was valued at $420 000 in 2022. It increased in value by 15% in 2023, then decreased by 10% in 2024. What is its value at the end of 2024?
    2. A school’s enrolment increased by 12% over two years. The enrolment is now 672. What was the enrolment two years ago?
    3. An athlete’s training run times decreased (improved) from 48 minutes to 42 minutes. What is the percentage decrease?
    4. A price is increased by 20%, then the new price is decreased by 20%. Is the final price equal to the original? Show your working and explain the result.
    5. In three consecutive years, a company’s revenue changes by: +15%, −10%, +8%. Starting from $200 000, what is the final revenue? Give your answer to the nearest dollar.
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