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Profit and Loss

Cost Price

Cost Price is the price at which an article is purchased by the buyer. It is abbreviated as C. P. In the calculation of Profit and loss, the value of cost price is very crucial. Here in the section we will try and understand what we mean by cost price and we will see several types of questions that can be formed on the concept. Let us begin.

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Cost Price

The money paid by the shopkeeper to the manufacturer or wholesaler to buy the goods is called the cost price (C. P.) of the goods purchased by the shopkeeper. If an article is purchased for some amount and these are to be added to the cost price. Such expenses are called overhead expenses or overheads. Profit and loss are always calculated on the basis of the cost price unless otherwise mentioned.

Cost Price

                                                                                                                                        Source: Youtube.com

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Some of the important formulae that we shall use throughout the chapter are below:

  1. Profit = S P  – C P
  2. Loss = C P  –  S P
  3. Profit percentage = [Profit/cost price] × 100
  4. Loss percentage = [loss/cost price] × 100
  5. S P = [(100 + gain%)/100]×C P = [(100 + loss%)/100]×C P
  6. C P = [100/ (100 + gain%)]×S P = [100/ (100 + loss%)]×S P
  7. S P = (100 +k) % of C P; where profit = k% of C P.
  8. S P = (100 – k)% of C P; where loss = k% of the C P.

Solved Examples

Q1: Find the cost price of an article which is sold for Rs. 220 at a loss of 12%.

  1. 250 rupees
  2. 333 rupees
  3. 125 rupees
  4. 210 rupees
  5. none of the above

Answer: Here the S P = Rs. 220, also we have loss =12%. Let the C P = Rs x. Then the S P = 88% of the C P. Thus we have:

220 = (88/100)× x. Simplifying this, we can see that x = 250. Therefore the cost price is = Rs. 250. Thus the correct option is A. rupees 250.

Questions on the cost price may also be asked by combining them with concepts like the marked price. To avoid loss due to bargaining by the customer and to get the profit over the cost price, a trader increases the cost price by a certain value. This increase in value over cost price is known as the markup and the increased price (i.e. C P + markup) is the marked price or the printed price or what we call the list price of the goods. The following formulae can be used to obtain C P from the marked price and vice versa:

Marked Price = C P + Markup

M P (Marked Price) = C P + (%markup on C P)

Q2: If the cost price of an article is Rs 300 and the percent markup is 20%. What is the marked price?

Answer: Here M P = C P + percentage markup on C P = 300 + 300 × [20/100]

Thus, M P = Rupees 360.

Alternate Questions

Sometimes you will encounter questions that don’t ask you what the C P is but rather ask you to derive another quantity from the C P. Let us see how to derive other quantities from C. P. We will also see some Cost price based questions below. Let us proceed.

Q1: A dealer gets the cost price of 15 oranges by selling 12 oranges. What is the percentage profit?

  1. 35%
  2. 12%
  3. 5%
  4. 25%
  5. None of the above

Answer: Profit percentage = [(goods left)/(goods sold)]×100 = [(15 – 12)/12]×100 = 25%. Therefore the profit is equal to 25% and the correct option is D. 25%

Q2: A trader sells all his articles at the cost price, but gives 10% less amount as he should give. What is his percentage profit?

  1. 11(11/12)%
  2. 12(1/11)%
  3. 11(1/9)%
  4. 9(1/11)%
  5. None of the above

Answer: Profit percentage = [(goods left)/(goods sold)]×100 = [(10/90)×100 = 11(1/9)%. Hence the correct option is D. 11(1/9)%.

We can see it like another way as discussed here. If we assume that the C P of 1 article is Rs 1. The trader gives only 90% of the articles instead of 100% and thus saves 10% articles. So his profit will be equal to the remaining articles (over the sold articles).

It means when he sells the articles (actually) worth Rs. 90 then he gains by articles worth Rs. 10. Hence profit percentage = [(10/90)×100] = 11(1/9) %

Also, the selling price = (100/90) = 10/9 = Rs. 1.11

Miscellaneous Questions

Q1: A person incurs 5% loss by selling a watch for Rs 1140. At what price should the watch be sold to earn 5% profit?                       [R R B, 2001]

  1. 1000 rupees
  2. 1280 rupees
  3. 1240 rupees
  4. 1255 rupees
  5. none of the above

Answer: Let the new S. P. be Rs x, then: (100 – loss percentage) : (Ist S P)  = (100 + Gain percentage) : (Second S P)

Thus we can write: [(100 -5)/1140] = [ (100 + 5)/x ]. Hence, simplification gives: x = [(105 × 1140)/95] = Rs. 1260. Therefore we can say that the new S P = Rs. 1260 and the correct option is E. None of the above.

Practice Questions

Q1: An article is sold at a certain price. By selling it at 2/3 of that price one loses 10%. Find the gain percent at the original price.

  1. 15%
  2. 20%
  3. 25%
  4. 30%
  5. 35%

Answer: E. 35%.

Q2: A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. What was the cost price of the article?         {S S C, 2004}

  1. 380 rupees
  2. 400 rupees
  3. 480 rupees
  4. 630 rupees
  5. none of the above

Answer: B. 400 rupees.

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