Profit & Loss: Basic Concepts

What does profit or loss mean?
Let us say you go to a shopping mall to buy a sweatshirt. You finalize the sweatshirt and are shocked to see its price tag. The price mentioned on the sweatshirt is Rs. 2500. You ask the owner to give some discount. He offers a discount of 20%.  Now just figure out, how much you will pay to the shopkeeper.
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Did you say 2000 rupees? You are bang on! You will pay a sum after subtracting 20% of amount written on price tag i.e. Rs. 500 from Rs. 2500. You finally pay the shopkeeper 2500 – 500 = Rs. 2000.  This example introduces you to the concept of marked price and discount. What you indirectly learned from this case is that the discount is calculated on the marked price only. Now let us assume here that the shopkeeper has purchased that sweatshirt for Rs. 1600. How much money that shopkeeper has earned by selling this sweatshirt? Now the shopkeeper has invested Rs. 1600 to buy this sweatshirt and finally sells for Rs. 2000. He makes a profit of Rs. 2000 – 1600 = Rs. 400. He earns this profit by putting in Rs. 1600 from his pocket that implies he makes a profit of 400 on his cost price of Rs. 1600. Thus his percentage profit is 100 × 400/1600 = 25%. This makes another concept of cost price and profit clear to you i.e. the price you put in from your pocket to buy a product is called cost price and the extra amount you get after selling the product is called the profit. The profit and loss percentage is calculated on cost price. Profit and loss problems are an integral part of all the competitive exams. You must understand the meaning of the basic terms used in profit and loss questions.
  • Cost Price (CP): The price, which is paid to acquire a product, is called cost price. All the overhead expenses (transportation, taxes etc.) are also included in the cost price.
  • Selling Price (SP): The sum of money, which is finally received for the product i.e. the price at which the product is finally disposed off is called the Selling price.
  • Marked Price (MP): The price, which is listed or marked on the product, is also known as quotation price/printed price/catalogue price/invoice price.
  • Profit:  If selling price is greater than Cost price, then excess of SP to CP is called Gain or Profit.
    E.g. Let the cost price of a quintal of rice be Rs 1000 and the shopkeeper sells the same for Rs 1125 per quintal, then profit = 1125 – 1000 = Rs. 125 per quintal.
  • Loss: If selling price is less than Cost price, then excess of CP to SP is called Loss.
    E.g. Let the cost price of a score of mangoes be Rs. 220. If the fruit vendor retails each mango for Rs. 10, then cost price per mango = Rs. 220/20 = Rs. 11/mango (As you know one score has 20 items)
    Selling price = Rs. 10 / mango ∴ Loss = Rs. 11 – Rs. 10 = Re. 1 per mango
    Note: Profit and loss percentage is always calculated on cost price, unless otherwise specified. Now let us come to profit loss formula in percentage, which will be followed by questions on profit and loss.
  • Profit percentage formula: The profit percent can be calculated as:
    Profit % = 100 × Profit/Cost Price.
  • Percentage Loss: The loss percent can be calculated as;
    Loss % = 100 × Loss/Cost Price.
  • Now let us solve some illustration to get idea about profit and loss aptitude questions. These illustrations will have the application of the profit and loss formula learned above.
Illustration 1:  An item is purchased for Rs. 1200 and is sold for Rs. 1400. How much profit is made on the same?
Sol: As given CP = 1200, SP = 1400. Profit = SP – CP ⇒ 1400 – 1200 = Rs. 200.
Illustration 2:  A chair is purchased for Rs. 6500 and is sold for Rs. 7500. How much profit is made on the same?
Sol: As given CP = 6500, SP = 7500. Profit = SP – CP ⇒ 7500 – 6500 = Rs. 1000.
Illustration 3:  A bottle is purchased for Rs. 80 and is sold for Rs. 65. What is his profit or loss in Rs?
Sol: As given CP = 80, SP = 65. Profit = SP – CP ⇒ 65 – 80 = Rs. - 15. This is in negative, just to convey that in this case, the person is making a loss. You can also apply loss = CP – SP formula to find the loss in positive value. Otherwise just follow one formula remembering a negative profit will always mean loss only. 
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Illustration 4:  A pen is purchased for Rs. 20 and is sold for Rs. 26. What is the percentage profit earned?
Sol: Here CP = 20, SP = 26. Profit = SP – CP ⇒ 26 – 20 = Rs. 6. 
Profit % = 100 × Profit/Cost Price ⇒ 100 × 6/20 = 30%.
Illustration 5:  A cup is purchased for Rs. 160 and is sold for Rs. 128. What is the profit or loss percentage?
Sol: Here CP = 160, SP = 128. Profit = SP – CP ⇒ 128 – 160 = -32. Again a negative profit of 32 means it is a loss.  
Profit % = 100 × Profit/Cost Price ⇒ 100 × (-32)/160 ⇒ = -20%. 
So there is a loss of 20%. You could have used the other formula also, which is explained above.
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