• Home
  • /
  • Blog
  • /
  • Profit & Loss(Meaning, Formulas & Examples)

Profit & Loss(Meaning, Formulas & Examples)

profit and loss formula

This post is also available in: हिन्दी (Hindi)

When you buy an item from a shop, the shopowner charges some amount for an item. The price at which the shopowner sells an item is not always the same as she/he bought the item. The difference between the price at which an item is bought and sold is known as profit or loss.

Every company and business works on the fundamental concept of profit and loss. It is very important to familiarize yourself with profit and loss, not only to run a business or company but also to keep an account of your own expenditure.

Let’s understand what profit and loss are and how it is calculated and learn about the profit and loss formula.

Profit and Loss Related Terms

When a person buys an article for a certain price and then sells it for a different price, she/he makes a profit or incurs a loss. There are various terms that are associated with this transaction, such as cost price(C.P.), selling price (S.P.), discount, marked price(or list price), profit, and loss. First, let’s start to understand these terms.

Cost Price(C.P.): The price at which an article is bought is called its cost price. For example, if a person buys a notebook for ₹$25$, this is called the cost price of the notebook and is abbreviated as C.P.

Selling Price(S.P.): The price at which an article is sold is called its selling price. For example, if a person sells the same notebook for ₹$30$, this is called the selling price of the notebook and is abbreviated as S.P.

Profit: When, in a transaction, the selling price is greater than the cost price, it means a person earns a profit, In the above example, the person made a profit of ₹$5$, as the selling price(₹$30$) is greater than the cost price(₹$25$) of the notebook.

profit and loss formula

Loss: When, in a transaction, the selling price is less than the cost price, it means a person incurs a loss, In the above example, if the person had sold the notebook for ₹$20$, then it would have been a loss of ₹$5$ for him, as S.P.(₹$20$) is less than the C.P.(₹25$) of the notebook.

profit and loss formula

Marked Price: Marked price is the price set by the seller on the label of the article. It is a price at which the seller offers a discount. After the discount is applied to the marked price, it is sold at a reduced price known as the selling price.

For example, you go to a shop and purchase a dress. The price tag on the dress is ₹$1,500$. This means the marked price(or list price) of the dress is ₹$1,500$.

profit and loss formula

Discount: In order to boost the sale of goods, shopkeepers offer discounts to customers. The rebate or the offer given by the shopkeepers to lure the customers is called a discount. Discount is always calculated on the marked price of the article.

$\text{Discount} = \text{Marked Price} – \text{Selling Price}$.

profit and loss formula

For example, you go to a shop and purchase a dress. The price tag on the dress is ₹$1,500$ and the shopowner offers to sell the dress for ₹$1,200$, then the discount on the dress is $1,500 – 1,200 =$₹$300$.

Is your child struggling with Maths?
frustrated-kid
We can help!
Country
  • Afghanistan 93
  • Albania 355
  • Algeria 213
  • American Samoa 1-684
  • Andorra 376
  • Angola 244
  • Anguilla 1-264
  • Antarctica 672
  • Antigua & Barbuda 1-268
  • Argentina 54
  • Armenia 374
  • Aruba 297
  • Australia 61
  • Austria 43
  • Azerbaijan 994
  • Bahamas 1-242
  • Bahrain 973
  • Bangladesh 880
  • Barbados 1-246
  • Belarus 375
  • Belgium 32
  • Belize 501
  • Benin 229
  • Bermuda 1-441
  • Bhutan 975
  • Bolivia 591
  • Bosnia 387
  • Botswana 267
  • Bouvet Island 47
  • Brazil 55
  • British Indian Ocean Territory 246
  • British Virgin Islands 1-284
  • Brunei 673
  • Bulgaria 359
  • Burkina Faso 226
  • Burundi 257
  • Cambodia 855
  • Cameroon 237
  • Canada 1
  • Cape Verde 238
  • Caribbean Netherlands 599
  • Cayman Islands 1-345
  • Central African Republic 236
  • Chad 235
  • Chile 56
  • China 86
  • Christmas Island 61
  • Cocos (Keeling) Islands 61
  • Colombia 57
  • Comoros 269
  • Congo - Brazzaville 242
  • Congo - Kinshasa 243
  • Cook Islands 682
  • Costa Rica 506
  • Croatia 385
  • Cuba 53
  • Cyprus 357
  • Czech Republic 420
  • Denmark 45
  • Djibouti 253
  • Dominica 1-767
  • Ecuador 593
  • Egypt 20
  • El Salvador 503
  • Equatorial Guinea 240
  • Eritrea 291
  • Estonia 372
  • Ethiopia 251
  • Falkland Islands 500
  • Faroe Islands 298
  • Fiji 679
  • Finland 358
  • France 33
  • French Guiana 594
  • French Polynesia 689
  • French Southern Territories 262
  • Gabon 241
  • Gambia 220
  • Georgia 995
  • Germany 49
  • Ghana 233
  • Gibraltar 350
  • Greece 30
  • Greenland 299
  • Grenada 1-473
  • Guadeloupe 590
  • Guam 1-671
  • Guatemala 502
  • Guernsey 44
  • Guinea 224
  • Guinea-Bissau 245
  • Guyana 592
  • Haiti 509
  • Heard & McDonald Islands 672
  • Honduras 504
  • Hong Kong 852
  • Hungary 36
  • Iceland 354
  • India 91
  • Indonesia 62
  • Iran 98
  • Iraq 964
  • Ireland 353
  • Isle of Man 44
  • Israel 972
  • Italy 39
  • Jamaica 1-876
  • Japan 81
  • Jersey 44
  • Jordan 962
  • Kazakhstan 7
  • Kenya 254
  • Kiribati 686
  • Kuwait 965
  • Kyrgyzstan 996
  • Laos 856
  • Latvia 371
  • Lebanon 961
  • Lesotho 266
  • Liberia 231
  • Libya 218
  • Liechtenstein 423
  • Lithuania 370
  • Luxembourg 352
  • Macau 853
  • Macedonia 389
  • Madagascar 261
  • Malawi 265
  • Malaysia 60
  • Maldives 960
  • Mali 223
  • Malta 356
  • Marshall Islands 692
  • Martinique 596
  • Mauritania 222
  • Mauritius 230
  • Mayotte 262
  • Mexico 52
  • Micronesia 691
  • Moldova 373
  • Monaco 377
  • Mongolia 976
  • Montenegro 382
  • Montserrat 1-664
  • Morocco 212
  • Mozambique 258
  • Myanmar 95
  • Namibia 264
  • Nauru 674
  • Nepal 977
  • Netherlands 31
  • New Caledonia 687
  • New Zealand 64
  • Nicaragua 505
  • Niger 227
  • Nigeria 234
  • Niue 683
  • Norfolk Island 672
  • North Korea 850
  • Northern Mariana Islands 1-670
  • Norway 47
  • Oman 968
  • Pakistan 92
  • Palau 680
  • Palestine 970
  • Panama 507
  • Papua New Guinea 675
  • Paraguay 595
  • Peru 51
  • Philippines 63
  • Pitcairn Islands 870
  • Poland 48
  • Portugal 351
  • Puerto Rico 1
  • Qatar 974
  • Romania 40
  • Russia 7
  • Rwanda 250
  • Réunion 262
  • Samoa 685
  • San Marino 378
  • Saudi Arabia 966
  • Senegal 221
  • Serbia 381 p
  • Seychelles 248
  • Sierra Leone 232
  • Singapore 65
  • Slovakia 421
  • Slovenia 386
  • Solomon Islands 677
  • Somalia 252
  • South Africa 27
  • South Georgia & South Sandwich Islands 500
  • South Korea 82
  • South Sudan 211
  • Spain 34
  • Sri Lanka 94
  • Sudan 249
  • Suriname 597
  • Svalbard & Jan Mayen 47
  • Swaziland 268
  • Sweden 46
  • Switzerland 41
  • Syria 963
  • Sao Tome and Principe 239
  • Taiwan 886
  • Tajikistan 992
  • Tanzania 255
  • Thailand 66
  • Timor-Leste 670
  • Togo 228
  • Tokelau 690
  • Tonga 676
  • Trinidad & Tobago 1-868
  • Tunisia 216
  • Turkey 90
  • Turkmenistan 993
  • Turks & Caicos Islands 1-649
  • Tuvalu 688
  • U.S. Outlying Islands
  • U.S. Virgin Islands 1-340
  • UK 44
  • US 1
  • Uganda 256
  • Ukraine 380
  • United Arab Emirates 971
  • Uruguay 598
  • Uzbekistan 998
  • Vanuatu 678
  • Vatican City 39-06
  • Venezuela 58
  • Vietnam 84
  • Wallis & Futuna 681
  • Western Sahara 212
  • Yemen 967
  • Zambia 260
  • Zimbabwe 263
Age Of Your Child
  • Less Than 6 Years
  • 6 To 10 Years
  • 11 To 16 Years
  • Greater Than 16 Years

Profit and Loss Formula

These are the important formulas that are used while solving profit and loss problems.

Profit Formula: If the selling price of an article is greater than its cost price, there is a profit(or gain) in the transaction. The basic formula used for calculating the profit is $\text{Profit} = \text{Selling Price} – \text{Cost Price}$ or $\text{Profit} = \text{S.P.} – \text{C.P.}$

Profit Percentage Formula: Many times the profit(or gain) is expressed as a percentage. The formula for profit percent or gain percent is

profit and loss formula

Loss Formula: If the selling price of an article is less than the cost price, there is a loss in the transaction. The basic formula used for calculating the loss is $\text{Loss} = \text{Cost Price} – \text{Selling Price}$ or $\text{Profit} = \text{C.P.} – \text{S.P.}$

Loss Percentage Formula: Many times the loss is expressed as a percentage. The formula for loss percent is

profit and loss formula

Note: Profit percent or loss percent is always calculated on the cost price (C.P.) of an item.

Selling Price Formula: When the cost price of an item and profit percent or loss percent is known, then the selling price of an item is calculated using the formula

profit and loss formula

Cost Price Formula: When the selling price of an item and profit percent or loss percent is known, then the cost price of an item is calculated using the formula

profit and loss formula

Examples

Ex 1: A man purchased a bicycle for ₹$840$ and sold it for ₹$800$. Find his gain/loss percent.

C.P. of bicycle = ₹$840$

S.P. of bicycle = ₹$800$

Since, $\text{S.P.} \lt \text{C.P.}$, therefore there is a loss in the transaction.

$\text{Loss} = \text{C.P.} – \text{S.P.} = 840 – 800 = $₹ $40$.

Ex 2: A man purchased a television set for ₹$15,800$ and sold it for ₹$18,170$. Find his gain/loss percent.

C.P. of television set = ₹$15,800$

S.P. of television set = ₹$18,170$

Since, $\text{S.P.} \gt \text{C.P.}$, therefore there is a profit in the transaction.

$\text{Profit Percent} = \frac{\text{S.P.} – \text{C.P.}}{\text{C.P.}} \times 100 = \frac{18,170 – 15,800}{15,800} \times 100 = 15$.

Therefore, the profit percent in selling the television set is $15\%$.

Ex 3: A bought a tape recorder for ₹$8,000$ and sold it to B. B in turn sold it to C, each earning a profit of 20%. What is the price paid for the tape recorder by C?

C.P. for A = ₹$8,000$

Profit for A = $20\%$

S.P. for A = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 20}{100} \times 8,000 =$₹ $9,600$.

S.P. for A = C.P. for B. => C.P. for B = ₹$9,600$

Profit for B = $20\%$

S.P. for B = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 20}{100} \times 9,600 =$₹ $11,520$

The price paid by C for the tape recorder is ₹$11,520$.

Ex 4: Reema bought a teapot for ₹$1,200$ and a set of cups for ₹$400$. She sold teapot at a profit of $5\%$ and cups at a loss of $5\%$. Find the amount received by her.

Teapot

C.P. = ₹$1,200$

Profit = $5\%$

S.P. = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 5}{100} \times 1,200 = \frac{105}{100} \times 1,200 = $₹$1,260$

Set of cups

C.P. = ₹$400$

Loss = $5\%$

S.P. = $\frac{100 – \text{Loss} \%}{100} \times \text{C.P.} = \frac{100 – 5}{100} \times 400 = \frac{95}{100} \times 400 = $₹$380$

Therefore, total amount received by Reema = $1,260 + 380 =$₹$1,640$.

Ex 5: By selling an item for ₹$1,12,000$, a man loses $40\%$. At what price he would have sold the item to earn a profit of $10\%$?

S.P. = ₹$1,12,000$

Loss = $40\%$

C.P. = $\frac{100}{100 – \text{Loss} \%} \times \text{S.P.} = \frac{100}{100 – 40} \times 1,12,000 =$₹$1,86,666.67$ 

Profit = $10\%$

S.P. = $\frac{100 + \text{Profit} \%}{100} \times \text{C.P.} = \frac{100 + 10}{100} \times 1,86,666.67 = $₹ $2,05,333.33$

Therefore, the man would have sold the item at ₹ $2,05,333.33$ to gain $10\%$ profit.

Ex 6: How much loss percent is earned by on selling $140$ geometry boxes at the loss of S.P. of $10$ geometry boxes?

Let the S.P. of $1$ geometry box = ₹$1$ 

So, S.P. of $140$ geometry boxes = $1 \times 140 =$ ₹$140$

Similarly, S.P. of $10$ geometry boxes = $1 \times 10 =$ ₹$10$

Loss = S.P. of $10$ geometry boxes = ₹$10$

Also, $\text{C.P.} = \text{S.P.} + \text{Loss} = 140 + 10 = $₹$150$

$\text{Loss}\% = \frac{\text{Loss}}{\text{C.P.}} \times 100 = \frac{10}{150} \times 100 = 6 \frac{2}{3}\%$.

Ex 7: The cost price of $10$ tables is equal to the selling price of $5$ tables. Find the profit percent in this transaction.

Let the $\text{C.P.}$ of $1$ table = ₹$1$

So, the cost of $10$ tables = $10 \times 1 =$₹$10$

C.P. of $10$ tables = S.P. of $5$ tables => Profit = Cost of $5$ tables = $5 \times 1 =$₹$5$

$\text{Profit}\% = \frac{\text{Profit}}{\text{C.P.}} \times 100 = \frac{5}{5} \times 100 = 100\%$.

Key Takeaways

These are the important formulas for solving problems on profit and loss

  • $\text{Profit} = \text{S.P.} – \text{C.P.}$ (Profit when S.P. > C.P.)
  • $\text{Loss} = \text{C.P.} – \text{S.P.}$ (Loss when S.P. < S.P.)
  • $\text{Profit} \% = \frac{\text{Proft}}{\text{C.P.}} \times 100$
  • $\text{Loss} \% = \frac{\text{Loss}}{\text{C.P.}} \times 100$
  • $\text{S.P.} = \frac{100 + \text{Profit} \%}{100} \times \text{C.P.}$
  • $\text{S.P.} = \frac{100 – \text{Loss} \%}{100} \times \text{C.P.}$
  • $\text{C.P.} = \frac{100}{100 + \text{Profit} \%} \times \text{S.P.}$
  • $\text{C.P.} = \frac{100}{100 – \text{Loss} \%} \times \text{S.P.}$
Unlike to Like Fractions

Conclusion

The term ‘Profit and Loss’ is a concept that is used in various real-life problems which take place in our lives almost every day. When an item is purchased at a greater price then a profit is incurred. Similarly, if an item is purchased at a lesser price then there is a loss.

Practice Problems

  1. Find the selling price of an item costing ₹$1,260$ if the loss is ₹$50$.
  2. Find the selling price of an item costing ₹$1,050$ if the profit percentage is $50\%$.
  3. A shopowner bought two sofa sets at ₹$15,000$ each and sells one at a profit of $10\%$ and the other at a loss of $10\%$. Find his overall profit or loss percent.
  4. A shopkeeper bought $200$ bulbs for ₹$10$ each. Out of those, $5$ bulbs were fused which he throw away. He sold the remaining at ₹ $12$ each. Find the percentage of gain or loss.
  5. Vimal bought a plot at ₹ $13,50,000$. He wanted an overall profit of $15\%$ but he sold one-third of the plot at a loss of $8\%$. At what price should he sell the remaining plot of land?

Recommended Reading

FAQs

What are profit and loss in math?

If an article is sold at a price higher than the price at which it was bought, there is a profit in the transaction and if an article is sold at a price lesser than the price for which it was bought, there is a loss. 

In other words, we can say that if Selling Price > Cost Price, there is a profit, and if Selling Price < Cost Price, there is a loss in the transaction.

What are the cost price and selling price?

The price at which an article is bought is called its cost price, and the price at which the article is sold is called its selling price.

How are profit and loss calculated?

Whenever the selling price of an item is greater than the cost price of an item, then there is a profit in the transaction. The formula to calculate profit is $\text{Profit} = \text{Selling Price} – \text{Cost Price}$.

Whenever the selling price of an item is less than the cost price of an item, then there is a loss in the transaction. The formula to calculate loss is $\text{Loss} = \text{Cost Price} – \text{Selling Price}$.

What is the profit and loss percentage formula?

Whenever the selling price of an item is greater than the cost price of an item, then there is a profit in the transaction. The formula to calculate profit percent is $\text{Profit} \% = \frac{\text{Profit}}{\text{C.P.}} \times 100$.

Whenever the selling price of an item is less than the cost price of an item, then there is a loss in the transaction. The formula to calculate loss percent is $\text{Loss} \% = \frac{\text{Loss}}{\text{C.P.}} \times 100$.

{"email":"Email address invalid","url":"Website address invalid","required":"Required field missing"}
>