1. Starter
Francesca used to earn £350 per week. Her pay rises to £ Frank used to earn £320. His pay rises to £ Who has had the greatest percentage increase?
A car costs £9750 when new. 5 years later it is sold for £4500. What is the average percentage decrease each year?

2. Reverse Percentages 18/10/2019
Recognise when a question requires reverse percentage method (rise and fall)
Use a reverse percentage method to find original price without a calculator
Use a reverse percentage method to find original price with a calculator

3. Reverse Percentages (Non Calc) Examples
Steve paid £54 for a pair of trainers that had been reduced by 40% in a sale. What was the original price?
Joanne paid £63 for a hotel room which was 10% cheaper than the normal price. What was the normal price?
60% =
£54
÷ 6 ÷6
10% = £9
x 100
100% =
£90
x 100

4. Reverse Percentages (Non Calc) Examples
Chloe’s shopping cost £96. This was 20% more expensive than last week. How much did she spend last week?
Darnell paid £66 for a train ticket this year. The price had risen by 10% from last year. What was the cost last year?
110% =
£66
÷ 11
÷11
10% = £6
x 100
100% =
£60
x 100

5. Practice: Non calculator
Pablo paid £81 for a family ticket at Drayton Manor, which gave him 10% off the full price. What is the full price?
A farmer notices the number of chickens born this year has risen by 20% to 360. How many were born last year?
90% = £81
10% = £9
100% = £90
120% = 360
10% = 30
100% = 300
Kat has noticed that the number of cars parked on her street has risen by 20% to 48. How many cars were parked on her street before?
Louisa paid £120 for a prom dress, which had 20% off in a sale. What was the original price?
120% = £48
10% = £4
100% = £40
80% = £120
10% = £15
100% = £150

6. What’s different about these numbers?
JD Sports15% discount
Price now £80.75
What’s different about these numbers?
Increase of12% to £44.80
Odeon Student 10% discount
Price now £6.21
Increase18% to £41.30
Nandos NUS 20% discount
Price now: £19.20

7. Original Amount = 100% value EXAMPLES (a) 85% = £43.90 1% = £0.5165
Jane paid £43.90 for a skirt that had been reduced by 15% in a sale. What was the original price?
85% =
£43.90
÷ 85
÷ 85
Decrease of 15%
85% value
1% =
£0.5165
x 100
x 100
100% =
£51.65
Original Price
(b)
Junior received a 8% pay rise. His new salary is £ What was his original salary?
108% =
£19200
÷ 108
÷ 108
Increase of 8%
108% value
1% =
£177.78
x 100
x 100
100% =
£17778
Original Salary 7

8. Find the original price. Be careful with increases and decreases!
JD Sports15% discount
Price now £80.75
Find the original price. Be careful with increases and decreases!
Increase of12% to £44.80
Odeon Student 10% discount
Price now £6.21
Increase18% to £41.30
Nandos NUS 20% discount
Price now: £19.20

9. JD Sports 15% discount
Price now £80.75
100% – 15% = 85%
85% = £80.75
1% = £0.95
100% = £95.00
CHECK!

10. 112 % = £44.80
1% = £0.40
100% = £40
Increase fare12% to £44.80
CHECK!

11. Odeon Student 10% discount
100% – 10% = 90%
90% = £6.21
1% = £0.069
100% = £6.90
Odeon Student 10% discount
Price now £6.21
CHECK!

12. Increase 18% to £41.30
118 % = £41.30
1% = £0.35
100% = £35.00
CHECK!

13. 100% – 20% = 80%
80% = £19.20
1% = £0.24
100% = £24.00
Nandos NUS 20% discount
Price now: £19.20
CHECK!

14. Calculator Reverse Percentages
Non-calculator
Reverse Percentages
Calculator Reverse Percentages