8th Class Mathematics Profit, Loss and Discount Profit, Loss and Discount

Profit, Loss and Discount

Category : 8th Class

*         Introduction


The term profit and loss are related to the business and marketing. If a merchant purchases a goods at a certain rate and sells it at the rate higher than the purchase price then he said to have earn profit and if he sells at the price less than the purchase price then he said to have loss.

In this chapter, apart from profit and loss we will also discuss about the tax which we have to pay on the goods we purchase from the market. The tax we pay on the goods we purchase is called as value added tax or VAT. The tax we pay as a vat is the nominal amount on the goods which goes to government funds and used by the government for providing the various facilities to the public such as road, electricity, water, and many other facilities.

The another term we will use in this chapter is discount. Discount is the amount reduced on the marked price of the article by the shopkeeper. The rate of discount is the rate at which the amount is reduced on the marked price. The marked price of the article is the price which is mentioned on the article or on the tag of the article. There is a difference between the mark price and cost price of the article. If MP > CP, then shopkeeper will have profit on that particular article on the other hand if MP < CP, then the shopkeeper will have loss on the article. Also if SP > CP, then it is profit and if SP < CP, then it is loss.  


*            Cost Price

The amount at which an article is purchased is called its cost price. It is denoted by C.P.

\[\text{C}.\text{P}.=\text{S}.\text{ P}.-\text{Profit}\]  


*            Selling Price

The amount at which an article is sold is called its selling price. It is denoted by S.P.

\[\text{Profit }=\text{S}.\text{P}.-\text{C}.\text{P}.\]

\[\text{Profit percent}=\frac{profit}{C.P.}\times 100\]

Also, \[S.P.=\left( \frac{100+\Pr ofit%}{100} \right)\times C.P.\]

\[\text{Loss }=\text{ C}.\text{P}.\text{ }-\text{S}.\text{P}.\]

\[\text{Loss Percent}=\frac{Loss}{C.P.}\times 100\]

\[S.P.=\left( \frac{100-Loss%}{100} \right)\times C.P.\]


*            Market Price

The price mentioned on an article is called market price. It is denoted by M P

\[\text{M}.\text{P}.=\text{ C}.\text{P}.\text{ }+\text{ Profit}\] Or, M.P. = S.P. + Discount


*            Discount

In order to increase the sale or clear the old stock some time the shopkeepers offer a certain percentage of rebate on the marked price this rebate is known as discount.

\[\text{S}.\text{P}.\text{ }=\text{M}.\text{P}.-\text{Discount}\]

\[\text{Discount }\!\!%\!\!\text{ =}\frac{Discount}{Markprice}\times 100\]

\[\text{Discount }\!\!%\!\!\text{ =}\left( \frac{M.P.-S.P.}{M.P.} \right)\times 100\]




  • The objects of mathematical study are continuity, infinity, infinity, infinitesimals and paradoxes.
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  • Even an uncorking clock shows right time twice in 24 hours.  




  • The price at which the article is bought is called cost price and the price at which it is sold is called selling price.
  • If the selling price is more than cost price then there is profit and if the selling price is less than the cost price then there is loss.
  • Discount is the relaxation of price given on the mark price of the item.
  • VAT is the tax charged on the mark price of the item when it is sold.  





  A man went to the market and purchased the different articles, among which he also purchased two freezes. He came to his home and found that there is some defect in one of the freezes and so he decided to sell both of them for Rs. 1500 each. He sold one of the freezes at the gain of 30% and other at the loss of 30%. Find the overall gain or loss on the whole transaction.

(a) 9.75%                                            

(b) 9.98%        

(c) 9.89%                                             

(d) 9.57%

(e) None of these


Answer: (c)  



  A merchant buys two kinds of coffee, one at the rate of Rs. 4000 per quintal and another at the rate of Rs. 1000 per quintal. He mixed them in a proportion of 10 kg and 6 kg respectively. If he wants to have a profit of 40% on the whole transaction, then at what price per quintal he must sell the mixture of the coffee from his outlet.

(a) Rs. 3500                                        

(b) Rs. 4580      

(c) Rs. 4850                                        

(d) Rs. 5280                        

(e) None of these


Answer: (a)        


Let the quantity of first kind mixed with the second kind be\[10x\]and\[6x\].

Then, C.P. of the mixture \[=\left( \frac{8000}{100}\times 10x+\frac{10000}{100}\times 6x \right)=Rs.\,1400x\]

\[\therefore \]Cost price of 1 kg of the mixture\[=\frac{1400x}{16x}=87.5\]

For the gain of 20%, S.P. of one kg of the mixture\[=\frac{40}{100}\times 87.5=35\]

S.P. of one quintal of coffee is = Rs. 3500  



  The price of the different articles in the market remains varying with the time. Mary went to the Mall and purchased some pulse and milk from there. She purchased 2 kg of pulse and 8 kg of milk for Rs. 900. After one month the price of pulse rose by 20% and that of milk by 100%, so she has to pay Rs. 1040 for the same quantity of the same article she purchased. Find the price per kg of pulse.

(a) Rs. 172.4                                       

(b) Rs. 150.6      

(c) Rs. 450.5                                       

(d) Rs. 285.2

(e) None of these  


Answer: (a)  


Let the cost of one kg of pulse be Rs. x and that of Milk be Rs. y.

Then cost of one kg pulse and four kg of milk \[=2x+8y=900\]

After increase in price of pulse and milk the cost will be\[=\text{1}.\text{2}x+\text{12y}=\text{1}0\text{4}0\]

On solving the above equation, we get \[x~=\text{172}.\text{4},\text{ y}=\text{69}.\text{4}\]  



  A shopkeeper buys two packets of dairy milk bar, each having same number of bars. The first packet was purchased at the rate of 30 paise each and second at the rate of 3 for 100 paise. The shopkeeper mixed both of them together and sold them at the rate of Rs. 8.50 per dozen. The shopkeepers gain or loss on whole transaction is:

(a) 85.25%                                          

(b) 123.68%      

(c) 120%                                              

(d) 52.8%

(e) None of these  


Answer: (b)  



  A dishonest merchant uses a defective weight balance to measure the weight of the article he purchased or sold at his outlet. When he purchases the goods for his outlet he uses to measure 10% less than the usual weight while selling the same goods he uses to measure 10% more than the usual weight. If he sells certain weight of goods to some one, his gain will be:

(a) 20%                                                

(b) 23%         

(c) 12%                                                

(d) 21%

(e) None of these  


Answer: (d)      

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