Three Types of GMAT Profit and Loss Problems

You will encounter the following three types of Profit/Loss problems in the GMAT:

Profit/loss as percentage of Cost Price

In this case you will be given the cost price and sales price, and will be asked to simply calculate the profit/loss incurred by the seller by entering into the given transaction. This will be done by dividing the difference between the Sales Price and the Cost Price by the Cost Price. To convert the decimal into a percentage, you will multiply it by 100.

Profit Percentage = ((Sales Price - Cost Price)/Cost Price) x 100

Selling price = Z x (Cost price)

Where Z is any positive number. When Z < 1 we have a loss. When Z = 1 we have neither profit nor loss. When Z > 1 we have a profit.

Profit or Loss % = (Z - 1) x 100.

Selling price = [(Y / 100) + 1]x (Cost price)

Where Y is the profit or loss percentage. When Y < 0 we have a loss. When Y = 0 we have neither profit nor loss. When Y > 0 we have a profit.

Profit/loss as percentage of Sales Price

Sometimes the problem will be worded differently and will require the test taker to calculate Profit Percentage for Seller, given the Sales Price and the Profit as a percentage of the Sales Price. In this case, user will first calculate the Cost Price based upon Sales Price and Sales Profit Percentage, and then calculate the Profit Percentage for the seller.

  Cost Price = (Sales Price) - (Sales Profit% x Sales Price)/100

Profit/loss as percentage as percentage of Marked Price

Another flavor of profit/loss questions that you will see on the exam will ask you to calculate Profit/loss based upon the marked price and may also ask you to take any discounts into consideration.

Let’s assume that Marked price (M) is known. Cost Price (C) is known. The profit percentage at the Marked Price is also given. The problem may ask you to calculate the discount applied to the transaction.

Before going into the formula understand the pricing chain:

Cost Price (from supplier) -> Marked Price (from retailer)-> Sales Price (from retailer; after discount)

Since (Discount = Marked Price – Sales Price), we need to determine the Sales Price to compute Discount.
 
Discount = Marked Price - Sales Price
              = Marked Price - ((Sales Profit % x Sales Price)/100 - (Cost Price))

Discount % = (Marked Price – Sales Price) / Marked Price

Note: The Sales Profit% is the Profit Margin

Contributions from: Luis R. Villegas H