1. Reverse Percentages
Finding the original price after deduction or increase
Let’s do the first one together:
A radio sells for £63, after a 40% increase in the cost price. Find the cost price.

2. Reverse Percentages
A radio sells for £63, after a 40% increase in the cost price. Find the cost price.
The selling price is 100% + 40%, so £63 = 140%.
Calculate 1%
140% = £63
1% = £63/140
1% = £0.45
The cost price is 100%, so multiply £0.45 by 100
Cost price = 0.45 x 100 = £45

3. Another example
A packet of washing powder is advertised as having '20% extra powder'. If it contains 1.32kg. What would the original pack contain?
1.02kg?
1.1kg?
1.06kg?
1kg?

4. Another example
A new car falls in value by 30% in a year. After a year, it is worth £8,400. Find the price of the car when it was new.
Remember that the original price of the car is 100%.
Original price = 100%.
Second-hand price = 100% - 30% = 70%.
So £8,400 = 70% of the original price.
So 1% of original price = £8,400 ÷ 70
Original price = 100% = 100 x 1% = 100 x (£8,400 ÷ 70)
= £12,000.

5. Footballers £ listing
The Association of Football has decided to re-price some of their footballers depending on their previous performance. Here are some of the new prices and their percentage increase or decrease:
Ronaldo 113.4m INCREASE 40%
Messi 160m DECREASE 20%
Di Maria 71.88m INCREASE 19.8%
Van Persie 18.75m DECREASE 25%
Neymar 57.5m INCREASE 9.8%
Falcao 40m INCREASE 5%
Can you work out any 3-6 players’ original prices before the re-pricing?