Applied Percents – Loss

Loss Mathematics
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In a previous lesson we looked at how Retailers place “Mark Ups” on items so that they can make a Profit on the sale.

It is important that you have viewed this lesson before doing the contents of our Loss Lesson.

The Mark Up and Profit Lesson can be viewed by clicking the link below:


Definitions for Items in Formulas


Cost Price

The Cost Price is how much it costs a retailer to buy items they are going to sell from suppliers or from overseas.


Mark Up

The Mark Up is extra money that the retailer adds on before putting a final price on the item.


Marked Price

This is the final price of the item. The Marked Price is then written onto the tag or sticker that is put onto the item in the shop.

This is the price the customer has to pay for the item and is also often called the full “Recommended Retail Price” or “RRP”.

If the item is NOT on discounted sale, then the customer has to pay the full RRP that is on the item’s tag or sticker.



If the shop is having a Sale, you do not have to pay the full Marked Price on the item. This is because the retailer gives you some money off the full normal price to create a lower than normal “Sale Price”.


Sale Price

The Sale price is the price the customer ends up paying for the item.

If the item is on sale for a discounted price, the Sale Price (sometimes called the “Selling Price”), will always be lower than the full normal Marked Price.

But if the item is not on sale, the customer will have to pay the full normal Marked Price.



Retailers sell items for more than it cost to get them, (even when the items are on Discount Sale). This allows the Retailer to make some money.

The money that the retailer makes from selling the item is called the “Profit”.



Sometimes a retailer will get into money problems, or have more items than they can fit in their shop or warehouse.

When this happens they have to sell goods at desperately low prices to get money to pay for shop rent, wages, electricity, transport, etc.

If they do not take this desperate step, they will get into huge debt and go out of business.

If they have to sell an item for less money than it originally cost them, then they will lose money on that item.

Losing money on a sale because the Sale Price is really really low, is called “Making a Loss”.


Dollar Loss

Tommy and Tamara TV Shop Pic
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Tommy and Tamara buy 100 “Retro TVs” at a Cost Price of $600 each.

They thought these TVs would be a real hit with young people and priced them with a Marked Price of $1000 each.

However, after two months they had only sold one TV set, and the other 99 TVs were taking up valuable space in their store room and gathering dust.

They then had to make the sad decision to sell the TV’s in a clearance sale at below cost with a Sale Price of $450.

This means that they do not make any Profit on each TV, instead they make a loss.

Discount Mathematics Six
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Percentage Loss

Just as we covered with “Profit” in a previous lesson, there are two ways to calculate Percentage Profit and Percentage Loss.

There are two ways businesses use to express Percentage Loss:

1) Percentage Loss based on the Cost Price


2) Percentage Loss based on the Selling Price

This can be very confusing for people new to Financial Mathematics. The trick is to read the given question or situation very carefully.

If the question just asks for “Percentage Loss” (and does not specify based on Selling or Cost), then calculate the Percentage Loss based on the Cost Price.

Shown below is how we calculate the Percentage Loss based on the Cost Price:

Discount Mathematics Seven
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Shown below is how we calculate the Percentage Loss based on the Selling Price

Discount Mathematics Eight
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Selling Price with Loss Formulas

We calculate the Selling Price for items which are being sold at a Loss as follows:

Discount Mathematics Nine
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Note that the above formulas are written in a format which should aloow direct entry of values into pocket calculators.


Loss Formulas Summary

Here are the main formulas we use for working with Losses.

Discount Mathematics Formula
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These need to be copied down into the maths notes for Losses in your workbook.


Profit and Loss Video

Here is a very comprehensive video about Profit and Loss with plenty of example questions in it.



Related Items

In our previous lesson we covered Cost Price, Mark Up, and Profit. Click the link below to check out this lesson.


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