To Learn the Profit and Loss formula from our best teachers. You can find the definition, formula, basic concept, calculation & solved examples. The profit and loss formula is used in mathematics to determine the price of an item in the market and understand how profitable the business is.
Every product has a cost price (C.P) and a selling price (S.P). Based on the values of these prices, we can calculate the profit or loss received for a particular product. The essential terms covered here are cost price, fixed, variable, semi-variable cost, selling price, marked price, list price, profit, loss percentage, etc.
Now, let’s go through the Profit and Loss formula with basic concept, formulas and Important notes.
Profit and Loss Formula
In mathematics, Profit and Loss are the formulas used to determine the price of a commodity in the market and understand how a business is profitable. Every product has a cost price (CP) and a selling price (SP). Based on the values of these prices, we can calculate the Loss incurred or the profit gained for a particular product.
For example, for a shopkeeper, if the cost price is more than the selling price, it becomes a loss, and if the value of the selling price (SP) is more than the cost price of a commodity, then it is a profit. In this article, you can see the Formulas related to Profit and Loss.
Basic Concept of Profit and Loss
Profit and Loss are terms used to identify whether a deal is profitable. In our daily life, we use these terms. Let’s learn profit and loss concepts in maths. It well explained below:
Profit: If the Selling price (SP) is greater than the cost price (CP), then the difference between the cost price (CP) and the selling price (SP) is called profit.
Loss: If the selling price (SP) is less than the cost price, then the difference between the Selling price and the cost price (CP) is called a Loss.
Cost Price (C.P)
The price paid for a product or commodity to purchase is called a cost price. The cost price also denoted as CP.
There are two types of cost price or CP.
- Fixed cost Price: It is the cost that does not register a change with an increase or decrease in the number of goods produced by a firm.
- Variable Cost Price: It is the cost that will show variations per the changes in the production levels.
Selling Price (S.P)
The price at which the product sold is called the Selling Price. It usually denoted as SP. Sometimes it’s also called a sale price.
Profit and Loss Formulas
Now, let’s find the profit formula and loss formulas.
Profit Formula: If the selling price of a product is more significant than its cost, there is a gain in the transaction. The basic profit formula given below:
- Profit = Selling Price (S.P) – Cost Price (CP).
Example: Let’s find the profit in a transaction if a product is bought at Rs 30 and sold at Rs 60. In this case, the Cost price = Rs 30; the Selling price = Rs 60.
Solution:
We know that,
Profit = Selling Price – Cost Price
Profit = 60 – 30 = 30.
Therefore, a profit of Rs 30 earned in the transaction. (Answer)
Loss Formula: If the selling price of a product is lesser than the cost price, there is a loss in the transaction. The basic Loss formula given below:
- Loss = Cost Price – Selling Price.
Example:
Let’s find the loss incurred if a product is bought at Rs 50 and sold at Rs 30. In this case, the Cost price = Rs 50; the Selling price = Rs 30.
Solution:
We know that,
Loss = Cost Price (CP) – Selling Price (SP)
Loss = 50 – 30 = 20.
Therefore, the loss incurred is $20. (Answer)
The formula for Profit and Loss Percentage (%)
The percentage (%) of profit or loss can calculated with the help of the following formulas, which indicate that the calculation of loss or profit in a transaction always based on its cost price. Some percentage profit and loss formulas given below:
- Profit percentage = (Profit /Cost Price) × 100
- Loss percentage = (Loss / Cost price) × 100
- S.P. or Selling Price = {(100 + P%)/100} × CP(if SP > CP)
- C.P. or Cost Price = {100/(100 + P%)} × SP(if SP > CP)
- S.P. or Selling Price = {(100 – L%)/100} × CP(if SP < CP)
- C.P. or Cost Price = {100/(100 – L%)} × SP(if SP < CP)
Important Notes
Some important notes related to profit and loss that we studied in this article given below:
Let’s have a look…
- Profit = SP – CP
- Loss = CP – SP
- Profit (%) = {Profit/CP} × 100
- Loss (%) = {Loss/CP} × 100
- Discount = Marked Price – Selling Price
- Discount (%) = (Discount/MP) × 100
Solved Problems based on Profit and Loss Formula
Question 1:
A man buys a fan for Rs. 1500 and it sells at a loss of 25 percent (%). Find the (SP) selling price of the fan?
Solution: The cost Price (CP) of the fan is Rs.1500
The loss percentage is 25%
As we know, Loss percentage = (Loss/Cost Price) x 100
25 = (Loss/1500) x 100
Therefore, loss = 375 rs.
As we know,
Loss = Cost Price – Selling Price
So, Selling Price = Cost Price – Loss
= 1500 – 375
Selling Price = Rs.1125/- (Answer)
Question 2:
A shopkeeper buys juice boxes in bulk at Rs.40 each and sells them at Rs.30 each. Calculate the loss and loss percentage using the profit-loss formula.
Solution:
To find: Loss and Loss Percentage
Given: Selling price = Rs 30; Cost price = Rs 40
Using the profit and loss formula, we know loss = C.P. – SP
Loss = 40 – 30 = 10 rs
Using the Loss Percentage Formula,
Loss% = (loss/C.P.) × 100
Loss Percentage = (10 /40) × 100
= 25%
Answer: Loss = Rs 10 and loss percentage = 25%.
Question 3:
If the cost of 8 pens equals the selling price of 6 pens, find the profit percent using the profit and loss formula.
Solution:
Let the C.P. of pens be a.
Then CP of 8 pens = 8a
CP of 6 pens = 6a
Given: S.P. of 6 pens = 8a
Using the profit and loss formulas,
Profit= SP- C.P.
profit = 8a – 6a = 2a
Profit % = (profit /C.P.) × 100
= (2a/6a)× 100 = 33.33%
Answer: Therefore, the profit % is 33.33%
Some Examples based on Profit and Loss Formula
Question 1:
Suppose a shopkeeper has bought 1 kg of Mangoes for 150 rs and sold it for Rs. 200 per kg. How much does he gain from the profit?
Solution:
Cost Price for apples is 150 rs.
The selling Price for apples is 200 rs.
Then the profit is ; P = SP – CP
P = 200 – 150 = Rs. 50/- (Answer)
Question 2:
A trader marks a discount of 20% on the Marked Price of Rs 120 for a commodity. What is the price at which he sells it after the discount?
Solution:
Given: Discount = 20%; Marked Price = $120; Selling Price = ?
Discount ($) = 20% on $120
Discount = (20/100) × 120
= 24 rs
Discount = Marked Price – Selling Price
S.P. = M.P. – Discount
S.P. = 120 − 24
Therefore, the price is 96rs. (Answer)
Question 3:
- Find the Selling price (S.P.) of a bicycle of Rs 800 if the loss is Rs 60
- If the Profit percentage is 60%
Solution:
1. C.P. = Rs 800
Loss = Rs 60
Let S.P. be x.
In case of loss, the cost price (C.P.) is more than the selling price (S.P.).
By using the formula of C.P. and S.P.
Loss = C.P. – S.P.
60 = 800 – x
or, x = 800 – 60
or, x = Rs 740
Thus, the S.P is Rs 740.
2. C.P. = Rs 800
Profit % = 60
Let the profit be x.
Profit % =profit / Cost price ×100
50 = x/ 800 × 100
or, 50 = x/ 8
Profit = Rs 400.
From the profit and loss formula,
Profit = S.P. – CP
Rs 400 = S.P. – 800
SP = 800 + 400
= 1200 rs
Thus, the S.P is Rs 1200 if the profit is 60% of the C.P. (Answer)
Practice Questions
1. A table sold at Rs. 5000 with 20% profit, find the gain or loss percentage if it had sold at Rs. 4500.
2. A dishonest dealer sells goods at a 20% loss on cost price but uses 30% less weight. Compute profit or loss percentage.
3. Suppose the CP of 30 pens is the same as the S.P. of some pens. If the profit is 35%, what is the number of pens sold?
4. A trader marks a discount of 50% on the Marked Price of Rs220 for a commodity. What is the price at which he sells it after the discount?
Suppose a shopkeeper has bought 2 kg of Apples for 250rs and sold it for Rs300 per kg. How much does he gain from the profit?
Looking for more formulas:
Pingback: Compound Interest- Formula, Definition, Derivation and Examples
Pingback: Compound Interest Formula- Definition, Derivation, Some examples