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

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