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Money & Finance · Lesson 8 of 14

Percentage Increase and Decrease

To increase by p% multiply by 1 + p/100. To decrease multiply by 1 - p/100. Percentage change is the change divided by the original.

What you will learn

  • Increase or decrease an amount by a percentage.
  • Find a percentage change.
  • Work backwards to the original amount.

Before you start: you should be able to find a percentage of an amount and know about sale prices. See Percentages and Discounts and Sale Prices.

The idea

To increase an amount by 20%20\% you end up with 100%+20%=120%100\% + 20\% = 120\% of the original, so multiply by 1.21.2. To decrease by 20%20\% you keep 80%80\%, so multiply by 0.80.8. These multipliers turn a two-step calculation into one.

Sorted into groups: Change, MultiplierChange: +10%, +25%, -10%, -25%. Multiplier: 1.1, 1.25, 0.9, 0.75.Change+10%+25%-10%-25%Multiplier1.11.250.90.75
Percentage changes and their multipliers. Increases are above 1 and decreases are below 1.

Percentage change

To find a percentage change, divide the change by the original amount and multiply by 100100.

Bar comparison of Before and AfterBefore is 12500; After is 13750. Longer bars are bigger amounts.Before12500After13750
A town grows from 12,500 to 13,750 people. The change is 1,250, which is 10% of 12,500.

Reverse percentages

If you know the amount after a change, divide by the multiplier to find the original. A price of £4545 after a 25%25\% rise was 45÷1.25=£3645 \div 1.25 = £36.

Why up then down does not cancel

A 50%50\% rise followed by a 50%50\% fall does not get you back to the start, because the second percentage is of a bigger amount.

Bar comparison of Start, After +50% and After -50%Start is 100; After +50% is 150; After -50% is 75. Longer bars are bigger amounts.Start100After +50%150After -50%75
100 rises to 150, then half of 150 comes off, leaving 75 and not 100.

Worked examples

Example 1: Percentage change

A town grows from 12 50012\,500 to 13 75013\,750. What is the percentage increase?

  1. Change: 13 750−12 500=125013\,750 - 12\,500 = 1250.
  2. Divide by the original: 1250÷12 500=0.11250 \div 12\,500 = 0.1.
  3. Multiply by 100100.

Answer: 10%10\% increase.

Example 2: Use a multiplier

A £240240 phone loses 35%35\% of its value in a year. What is it worth then?

  1. A decrease of 35%35\% leaves 65%65\%, so multiply by 0.650.65.
  2. 240×0.65=156240 \times 0.65 = 156.

Answer: £156156

Example 3: Reverse percentage

After a 25%25\% price rise a concert ticket costs £4545. What was the original price?

  1. 1.25×original=451.25 \times \text{original} = 45.
  2. 45÷1.25=3645 \div 1.25 = 36.

Answer: £3636

Tip: always divide the change by the original value, not the new one.

Why it matters

Pay rises, price changes, population growth and falling stock values are reported as percentage changes. Multipliers are also the key idea behind compound interest, where the same multiplier is applied again and again.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.

Question 1 of 8

Increase 8080 by 10%10\%.

Question 2 of 8

Decrease 200200 by 25%25\%.

Question 3 of 8

A price rises from 4040 to 5050. What is the percentage increase? Give the number only.

Question 4 of 8

A price falls from 6060 to 4545. What is the percentage decrease? Give the number only.

Question 5 of 8

What is the multiplier for an increase of 8%8\%?

Question 6 of 8

Rent of £500500 goes up by 4%4\%. What is the new rent, in pounds?

Question 7 of 8

After a 25%25\% rise a ticket costs £4545. What did it cost before, in pounds?

Question 8 of 8

A price rises by 50%50\% and then falls by 50%50\%. How does the final price compare with the start?

Choose one answer