2.04 Consumer percentages

When buying products, two things that are important to understand are mark ups and discounts.

A mark up is a percentage increase in the price of a product.

A discount is a percentage decrease in the price of a product.

A mark up indicates that the price of the product has increased from its original price and the percentage of the mark up indicates by how much. For example: if the price of a jumper has been marked up by 20\%, then its price has been increased by 20\%.

Similarly, the percentage of a discount indicates how much the price of a product has decreased from its original price.

Since mark ups and discounts are simply  percentage increases and decreases  , we can calculate them using the same methods.

Examples

Suppose a video game was marked up by 20\%, later discounted by 25\% and finally discounted again by 40\%. If the original price of the video game was \$50, what is its current price?

• The video game starts at the price of \$50.

• After a mark up of 20\%, its price is \$50\times 120\% which is equal to \$60.

• After a discount of 25\%, its price is \$60\times 75\% which is equal to \$45.

• After a final discount 40\%, its price is \$45\times 60\% which is equal to \$27.

So the current price of the game is \$27.

However, this is a lot of steps. Notice that the only operation we applied to the price was multiplication. Since multiplication does not need to be applied one at a time, we can reach the same answer by calculating:\text{Current price} = \$50\times 120\%\times 75\%\times 60\%

The advantages of this approach are that we can cancel out factors if we convert the percentages into fractions, or simply use a calculator to evaluate the expression in one step. Since the order in which we multiply doesn't matter either, we can also choose which percentage changes we want to apply first to make calculations easier.

Mark ups and discounts of the same percentage do not cancel each other out.

For example: if an item is marked up by 10\% and then discounted by 10\%, its final price will be:\text{Final price}=\text{Original price}\times 110\% \times 90\%

Evaluating the left hand side, we get:\text{Final price}=\text{Original price} \times 99\%

As we can see, the final price and the original price are not the same.

Examples

Almost everything we buy has a compulsory \$10 mark-up applied to it, called goods and services tax (GST). The extra money we pay goes to the government, and they can spend it on essential things like schools and roads. Some items we buy are excluded from GST. The most common examples are fresh fruit and vegetables, as well as other basic foods such as bread, flour, oil, and dairy products.

We can calculate the total price, inclusive of GST, in the same way we calculate percentage increases.

GST is a 10\% price increase.

Examples