A percentage change to obtain a new value followed by another percentage change will give a different result to adding the two percentages together.
£100 is increased by 10%. The answer to that calculation is increased by 20%.
What is the difference between that calculation and simply increasing the amount by 30%?
The multiplier for the 10% increase is 1 + `frac(10)(100)` = 1.1
£100 x 1.1 = £110
The multiplier for the 20% increase is 1 + `frac(20)(100)` = 1.2
£110 x 1.2 = £132
The multiplier for the 30% increase is 1 + `frac(30)(100)` = 1.3
£100 x 1.3 = £130
The difference is £132 - 130 = £2
Answer: £2
A shop reduces the price of a jacket by 30%. At the end of the sale, the shop increases the price of the jacket by 30% from its sale price.
Prove that the jacket is now cheaper.
The reason for the difference is that the original value before the sale was £100, and the percentage was based on that value.
After the sale, the original value was £70, and the percentage was based on that lower value.
Answer:
Say original price was £100
Multiplier for sale price is 1 - `frac(30)(100)` = 0.7
Sale price = £100 x 0.7 = £70
At end of sale, price raised by 30%
Multiplier is now 1 + `frac(30)(100)` = 1.3
New price = £70 x 1.3 = £91