Percentage increase
A bill of £80.00 increases by 15%. What is the new bill?
- Find 15% of £80.00: 0.15 × 80 = £12.00.
- Add the increase: £80.00 + £12.00.
Answer: The new bill is £92.00.
Back to National 5
Topic
Numeracy and Practical Problem Solving
Percentages are used to compare real changes in prices, wages, tax, VAT, profit, loss, and discounts.
Topic explanation
Read whether the percentage makes the value go up or down. A discount reduces a price; VAT usually increases a price.
For reverse percentages, the number you are given is not the original amount. Work back from the final percentage.
In exam-style Applications questions, the method matters because the answer is used to make a decision about cost, profit, or value.
Quick methods
- Increase
- Find the percentage amount, then add it.
- Decrease
- Find the percentage amount, then subtract it.
- Reverse percentage
- Divide by the final percentage written as a decimal.
- VAT and discount
- Apply the steps in the order stated in the question.
Worked examples
Discount
A jacket costs £60.00 and has 25% off. What is the sale price?
- 25% is one quarter.
- £60.00 divided by 4 = £15.00 discount
- £60.00 − £15.00 = £45.00
So: The sale price is £45.00.
Reverse percentage
A sale price is £72.00 after a 20% discount. What was the original price?
- After a 20% discount, £72.00 is 80% of the original.
- 80% as a decimal is 0.80.
- £72.00 divided by 0.80 = £90.00
Final step: The original price was £90.00.
Exchange rate decision
A pupil changes £180 into euros at €1.14 for £1. A €12 fee is then taken. How many euros are left?
- Convert the pounds first: 180 × 1.14 = €205.20
- Subtract the fee: €205.20 − €12.00 = €193.20
Answer: The pupil has €193.20 after the fee.
Watch out: Apply the fee in the currency stated. Here the fee is in euros, so it is subtracted after converting.