Profit and loss formula is one of the most important mathematical formulas which are used to calculate many maths problems in our academic and daily life. These formulas have high usage in small and large businesses, retails and those related to finance apart from the calculations involved in our schools and college life.
In retails, profit and loss formulas are applicable to determine the price of a commodity in the market. Every product in the market has a cost price and selling price. With the help of the values of these prices, we can calculate the profit gained and also the loss of money in a particular product. For any shopkeeper or seller, if the value of selling price is more than the cost price of a commodity, then its a profit to him and if the value of cost price is more than the selling price, then its a loss for him.
There are a number of terminologies when we discuss profit and loss formula. They are cost price, selling price, profit or gain, loss, profit percentage or gain percentage, loss percentage, marked price, variable cost, fixed cost, discounts & discount percentage etc. Profit and loss questions for class 8 covers all these terms which are inclusive of the class 8th syllabus.
Here, in this article, we will discuss all the formulas which will help you to solve profit and loss problems along with tricks and shortcuts. Keep reading the article below.
Before learning the formulas for profit and loss, let us discuss a few general terms used in the formulas for better understanding.
Cost price: The amount paid for a product.
Selling Price: The amount at which the product is sold
Marked Price: The price mentioned by the shopkeeper more than the selling price, to give a discount to the buyer.
Profit: The amount gained after selling the product more than its cost price
Loss: When the product is sold and the selling price is less than the cost price, then it is said, the seller has incurred a loss.
Now let us learn the profit and loss formulas with some tricks to remember all of them.
Profit or Gain = Selling Price – Cost Price (Selling Price > Cost Price) 
Loss = Cost Price – Selling Price (Cost Price > Selling Price) 
%Profit = (Profit /Cost Price)Ã— 100 
%Loss = (Loss / Cost price) Ã— 100 
Discount = Marked Price â€“ Selling Price 
%Discount = (Discount/Marked price) Ã— 100 
Apart from these formulas, there are some tricks by means of which you can easily solve profit and loss problems.
Let us call Selling Price as SP, Cost price as CP, Marked Price as MP, Profit as P and Loss as L. Now,
 SP = \(\frac{100+P}{100}\) Ã— CP
 SP = \(\frac{100 – L}{100}\) Ã— CP
 CP = \(\frac{100}{100 + P}\) Ã— SP
 CP = \(\frac{100}{100 – L}\) Ã— SP
 Discount = MP â€“ SP
 SP = MP – Discount
 For false weight, profit percentage will be
P% = \(\frac{True Weight – False weight}{False weight}\) Ã— 100.
 When there are two successful percentage profits say m% and n%, then the net percentage profit equals to:\(\frac{m+n+mn}{100}\)
 When the profit is m% and loss is n%, then the net percentage profit or loss will be: \(\frac{mnmn}{100}\).
 If a commodity is sold at m% profit and then again sold at n% profit then the actual cost price of the commodity will be;
CP = \(\frac{100*100*P}{(100+m)(100+n)}\)
In case of loss,
CP = \(\frac{100*100*P}{(100m)(100n)}\)
 If P% and L% are equal then,
P=L
And %loss = \(\frac{P^2}{100}\)
Based on the abovegiven formulas, let us solve profit and loss problems with solutions here.
Problem 1: A person purchased an article for â€Žâ‚¹ 100. If he sells it at a 15% profit then find his selling price.
Solution: SP = CP [ 1 + ( Gain % x 100) ]
SP = 100 [ 1 + (15/100) ]
= 100 x 1.15
= 115.
The article selling price is â‚¹ 115.
Problem 2: If the cost of 25 pens is equal to the selling price of 15 pens. what is the gain or loss%?
Solution: The Profit percent = [ pens left / pens Sold ] x 100
Profit % = [ ( 25 – 15) / 15 ] x 100 = 10 Ã— 100 / 15 = 1000/15 = 66.67%
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