GMAT word problems on profit and loss are quite common in the Quant section of the exam. You will need to learn about the concepts of cost price and selling price of a product along with a few important formulae. These will help you to solve the problems in this section in a quicker and faster manner. You will encounter problems which are not very simple or straightforward, so we have listed out a few important formulas and questions with solutions below that are certain to assist you in answering these questions in the GMAT exam.
So let us look at some of the formulas.
Profit & Loss Formulae
Cost price (CP) is the price at which an article is purchased or produced. Selling price (SP) is the price at which an article is sold.
If SP > CP, it is a profit or gain. If CP > SP, it is a loss.
Gain or Profit = SP > CP
Loss = CP > SP
Loss or gain is always calculated on CP or by using the CP as the base.
Profit Percentage (Profit %):
Loss Percentage (Loss %) :
In the case of a gain or profit,
The following are the 3 main types of problems which you are likely to come across in this section :
Profit/Loss percentage as percentage of Marked Price
You will be asked to calculate the Profit or loss based on the Marked Price of the object. If there are any discounts, then you will have to take that into consideration as well.
Let us assume Marked Price as M, Cost Price as C. The known values are Marked price, cost price and profit percentage. You will be asked to calculate the discount applied on the transaction.
Discount = Marked Price – Sales Price. We will need to determine the Sales Price to calculate the Discount.
Profit/Loss percentage as percentage of Cost Price
In these types of questions you will be provided with cost price and sales price and then asked to calculate the profit or loss which is incurred by the seller in the given transaction. This is calculated by dividing the difference between the Sales price and Cost price by the cost price (i.e)
(Sales price – Cost Price) /Cost Price.
If you would like to convert the decimal to percentage you can multiply the same by 100.
Profit/Loss percentage as percentage of Sales Price
You will be asked to calculate the cost price based on the Sales price and Sales profit percentage. Then you can calculate the profit percentage of the seller.
Memorizing these formulas is a good GMAT word problems strategy as it makes solving questions easier and faster.
GMAT Math Word Problems – Profit & Loss Sample Questions:
- If the selling price of 25 goods is equal to the cost price of 20 goods, what is the % of loss or profit made?
Let the CP of 1 article be Rs.1.
Hence, CP of 20 goods = 20 * 1 = Rs. 20
SP of 25 goods = cost price of 20 goods = Rs.20.
Let us find the CP of 25 goods.
Cost price of 25 goods = 25 * 1 = Rs. 25.
Therefore, profit made on sale of 25 goods = Selling price of 25 goods – cost price of 25 goods = 20 – 25 = – Rs. 5.
Because the profit is negative, it is a loss of Rs. 5.
Therefore, % loss = (Loss /CP )* 100
% loss = 5/25 * 100 = 20% loss.
- Sam purchases 10 apples for Rs. 1. At what price should he sell a dozen apples if he wants to make a total profit of 25%?.
The CP of 1 apple = 1/10 or Rs. 0.10.
As Sam wants to make a profit of 25%, his SP per apple should be 0.10 + 0.25* 0.10 = 0.1 + 0.025 = Rs. 0.125.
If the SP of 1 apple is Rs. 0.125, the SP of a dozen apples = 12 * 0.125 = Rs. 1.5
- What is the maximum percentage discount that a shopkeeper should offer on his quoted price so that he ends up selling at no profit or loss, if he had initially quoted his goods up by 50%?
Let the CP of the goods be Rs. 100.
He initially quoted his goods up by 50%.
Therefore, a 50% markup would have resulted in his quoted price being Rs.100 + 50% of Rs. 100 = Rs. 100 + Rs. 50 = Rs. 150.
He sells the product at no profit or loss.
Therefore, he sells the product at CP, which is RS. 100.
Hence, he offers a discount of Rs. 50 on her marked price of Rs 150.
Hence, the % discount offered by her = (Discount/ Marked Price) *100 = (50/150) *100= 33.33%
- A dealer who marked his commodity up by 50% subsequently offered a discount of 20% on the quoted price. What is the percentage profit the merchant made after offering the discount?
The easiest way is to assume a value for the merchant’s cost price.
Therefore, it is best to assume the cost price to be Rs. 100.
The merchant marks his commodity up by 50%.
Therefore, his marked price (quoted price) = cost price + mark up.
Marked price = Rs. 100 + 50% of Rs. 100 = 100 + 50 = Rs. 150.
The merchant gives a discount of 20% on his quoted price.
Discount offered = 20% of 150 = Rs. 30.
Therefore, he sold his commodity for Rs. 150 – Rs. 30 = Rs. 120.
We assumed his cost to be Rs. 100 and he sold it finally for Rs.120.
Hence, his profit = Rs. 20 on his cost of Rs. 100.
Hence, his % profit = profit/CP * 100 = (20/100) * 100 = 20%.
GMAT word problems on profit and loss are easy to solve if you are thorough with the formulas and practice them well enough. You can check out some GMAT word problems practice questions or you can even download some GMAT word problems pdf from various credible sources online and practice them until you are perfect.
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