Profit and Loss with Formulas, Percentage & Solved Examples
Profit and loss terms are used to identify whether a sale is advantageous or not. We all are somewhat familiar with the concepts of profit and loss, when a person runs a business, he or she either faces loss or earns profits. When a person sells a product at a higher rate than the cost price, the difference between both amounts is called profit. On the other hand, when a person sells a product at a lower rate than the cost price, then the difference between both amounts is called loss.
What are Profit and Loss?
Profit and loss terms are used to identify whether a sale is advantageous or not. We apply these phrases very frequently in our daily lives. Every commodity, product or item has a cost price and selling price and depending on the values of these prices, we compute the profit gained or the loss incurred for an individual product.
Profit: When a person sells a product at a higher rate than the cost price, then the difference between both amounts.
Profit = Selling price – Cost price
Loss: When a person sells a product at a lower rate than the cost price, then the difference between both amounts.
Loss = Cost Price – Selling Price
Important Definitions of Profit and Loss
Cost Price: Cost price is the price at which a person purchases a product. For example, if Ahana purchased a book for 250 rupees, this is the cost price for that particular book. Cost price is abbreviated as C.P.
Selling Price: Selling price is the price at which a person sells a product. For example, if Ankur sold a book for 350 rupees, then this is thought to be the selling price of the book. The selling price is abbreviated as S.P.
Market Price: It is the price that is marked on an article or commodity. It is also known as list price or tag price. If there is no discount on the marked price, then the selling price is equal to marked price.
Markup: It is the amount by which cost price is increased to reach market price. Markup = market price – cost price
Discount: The reduction offered by a merchant on marked price is called a discount.
Successive Discount: If an article is sold at two discounts then it is said that it is sold after two successive discounts.
Dishonest Dealing: In it, a person/shopkeeper sells any product at the wrong weight and earns a profit. This can be done either by using false weight or by false reading.
1) A shopkeeper claims to sell rice at a cost price but uses a false weight of 900gm instead of 1000gm.
2) A person sells cloth to customer but uses false reading and gives 90 meters of cloth instead of 100 meters.
Successive Selling: In it, a product is sold for more than one time from one person to another person at some profit or loss. For example – A sold a pen to B at 10% profit and then B sold the pen to C at 20% profit.
Sales Tax: When purchasing any product we have to give certain tax to the government. This additional payment is known as sales tax. Tax is always calculated on the selling price of a product.
Profit and Loss Formulas
Profit and loss formula is employed in maths to determine the price of an entity in the market and comprehend how advantageous a business is.
If the selling price > cost price, then the difference between the S.P. and C.P. is called profit.
Similarly, if the selling price < cost price, then the difference between the C.P. and the S.P. is called loss.
Profit and Loss Terminologies | Meaning | Formulas |
Profit or Gain | The selling price of the object > than its cost price | Profit=Selling price(SP) – Cost Price(CP) |
Loss | The cost price of the object > than its selling price | Loss=Cost Price(CP) – Selling Price(SP) |
Selling Price | The piece for which a commodity is sold is said to be the selling price for that particular item denoted as SP. | \(SP=\left(\frac{100+\text{Profit}\%}{100}\right)\times CP\) OR \(SP=\left(\frac{100-\text{Loss}\%}{100}\right)\times CP\) |
Cost Price | The expense at which an object is bought is termed as the cost price for that object, abbreviated as C.P. | \(CP=\left(\frac{100}{100+\text{Profit}\%}\right)\times SP\) OR \(CP=\left(\frac{100}{100-\text{Loss}\%}\right)\times SP\) |
Discount | To manage the competitors in the industry and promote the sale of goods, vendors offer discounts to consumers. | Discount= MP – SP(Marked Price – Selling Price) |
Profit Percentage and Loss Percentage
The profit percentage (%), as well as the loss percentage (%), is obtained with the help of the below-mentioned formulas. Along with the profit percentage (%) and loss percentage (%) other percentage-related formulas are also discussed below:
Profit and Loss Terminologies | Formulas in Percentage |
Profit percentage(%) | Profit=(SP) – (CP) \(\text{Profit percentage}\%=\left(\frac{\text{Profit}}{\text{Cost Price}}\right)\times 100\) |
Loss percentage(%) | Loss= (CP) – (SP) \(\text{Loss percentage}\%=\left(\frac{\text{Loss}}{\text{Cost Price}}\right)\times100\) |
Discount (%) | \(\left(\frac{\text{Discount}}{\text{Marked Price}}\right)\times100\) |
Markup (%) | \(\left(\frac{\text{markup}}{\text{cost price}}\right)\times 100\) Where Markup = Selling Price – Cost |
For false weight, the profit percentage can be determined by the formula:\(\text{Gain}\%=\frac{\text{Error}}{\text{TrueValue}-\text{Error}}\times100\%.\)
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Profit and Loss Tips and Tricks
Candidates can find different tips and tricks below for solving the questions related to profit and loss.
Tip # 1: Candidates need to make sure that they know all the important formulas related to profit and loss which are discussed above and some are mentioned below.
- If ath part of items are sold at x% loss, then for making no profit no loss, Required gain percentage in selling rest items = ax/(1-a)
- If two objects are sold at same selling price, one at x% profit and other at x% loss, then Loss % = \(\frac{X^2}{100}\)
- If the cost price of x articles is equal to selling price of y articles, then Profit percentage = {(x-y)/y} x 100
Tip # 2: If there are two successive profits or losses at x% and y% respectively, then the resultant profit or loss% = (x + y + xy)/100
- For profit, we take x and/or y as +ve value
- For loss, we take x and/or y as –ve value
Tip # 3: Profit percentage and loss percentage are always calculated on C.P. unless stated otherwise.
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Also, check this video on Profit and Loss for better clarity on the topic!
Solved Examples of Profit and Loss
Example 1: Marked price of a cricket bat is Rs 1000 and it is sold at Rs 800. Find the discount percentage.
Solution: Discount = MP – SP = 1000 – 800 = Rs 200
Discount Percentage = (D/MP) × 100 = (200/1000) × 100 = 20%.
Example 2: Marked price of a product is Rs 240 and 25% of discount is provided on it. Find the selling price.
Solution: Discount = SP × 25% = 240 × (25/100) = Rs 60
Selling price = MP – Discount = 240 – 60 = Rs 180.
Alternate Method:
Selling Price = (100 – D %) × MP/100 = (100 – 25) × 240/100 = Rs 180.
Example 3: A T-shirt is sold after providing two successive discounts of 20%. If marked price of a T-shirt is Rs 200 then find the selling price.
Solution: Discount 1 = 200 × 20/100 = Rs 40
Selling price after 1st discount = 200 – 40 = Rs 160 Discount 2 = 160 × 20/100 = Rs 32
Selling price after 2nd discount = 160 – 32 = Rs 128
Alternate Method:
Effective discount = 20 + 20 – (20 × 20)/100 = 36% Discount = 200 × 36/100 = Rs 72
Selling price = 200 – 72 = Rs 128.
Example 4: A man gains 30% by selling an article for a certain price. If he sells it at double the current selling price, then what will be the profit percentage?
Solution: Let, the cost price be Rs. x.
∴ Selling price = Rs. 1.3x
Now, new SP = Rs. 2.6x
∴ Profit % = [(2.6x− x )] × 100 = 160%
Example 5: If A bought an article at Rs.200 and sold it to B at 20% profit. Again B sold the article at 10% profit to C. Find the amount paid by C.
Solution: Price paid by B = 200 + (200/100 × 20) = 200 + 40 = Rs. 240
∴ Price paid by C = 240 + (240/100 × 10) = 240 + 24 = Rs. 264
Alternate Method:
Net profit = 20 + 10 + 20 × 10/100 = 32%
Hence, amount paid by C = 200 + (200/100 × 32) = Rs. 264.
Example 6: A man sold 2 bicycles at the same selling price. One at 20% loss and other at 20% profit. Find overall profit and loss percentage.
Solution: Let selling price be 300x
Then, CP for 1st bicycle = 250x Then, CP of 2nd bicycle = 375x
Hence, Net CP = 625x and net SP = 600x
∴ Net loss % = (25x/625x) × 100 = 4%
Example 7: If the cost price of 5 oranges is equal to the selling price of 4 oranges, then find a profit percentage?
Solution: Let cost price of an orange is Rs. 4 and selling price of an orange is Rs. 5 (we can assume it as it satisfies the given condition of the cost price of 5 oranges is equal to selling price of 4 oranges)
Hence, profit percentage = [(5 – 4)/4] × 100 = 25%
Example 8: 10 pens costs Rs. 100 each. If half of the pens are sold at 10% loss then find at what price remaining each pens should be sold for making no loss and no profit.
Solution: Total cost price of 10 pens = 10 × 100 = Rs. 1000
Selling price of 1 pen = 100 – (100 × 10%) = Rs. 90 Hence, selling price of 5 pens = Rs. 450
Now, selling price of remaining 5 pens = 1000 – 450 = Rs. 550 Hence, selling price of 1 pen = Rs. 110
∴ Profit % = [(110 – 100)/100] = 10%
Example 9: Ram purchased a bicycle for Rs. 5954. He had paid a VAT of 14.5%. Find the list price of the bicycle.
Solution: Let the list price be Rs. a. VAT = 14.5%
So, a × (114.5/100) = 5954
⇒ a = (5954 × 100)/114.5
⇒ a = 5200
∴ The list price of the bicycle was Rs. 5200.
Example 10: Rajesh bought accessories worth Rs. 150. Out of the amount spent for buying accessories, Rs. 10 was spent on sales tax due to taxable purchases. If the tax rate was 10%, calculate the price of the tax-free items.
Solution: Total Price = 150 Tax paid = Rs. 10 Tax = 10%
Let the taxable purchases = Rs x
⇒ 10% of x = 10
⇒ 0.1x = 10
∴ x = 100
∴ Tax free items = 150 – 100 – 10 = Rs.40
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FAQs of Profit and Loss
Profit percentage = (Profit /Cost Price) x 100.
Loss percentage = (Loss / Cost price) x 100.
Cost price formula = Selling Price + Loss.
Discount = Marked Price – Selling Price