Profit and loss are the terms related to monetary transactions in trade and business. Whenever a purchased article is sold, then either profit is earned or loss is incurred.
Cost Price (CP) :This is the price at which an article is purchased or manufactured.
Selling Price (SP): This is the price at which an article is sold.
Profit (SP>CP) :When an article is sold at a price more than its cost price, then profit is earned.
Loss (CP>SP) :When an article is sold at a price lower than its cost price, then loss in incurred.
Note : Profit and loss always calculated on cost price.
Some Important Concept
1. If a person sells two similar articles, one at a gain of a% and another at a loss of a%, then the seller always incurrs a loss which is given by Loss%=(a/10)^2 %
2. If a'th part of some items is sold at x% loss, then required gain per cent in selling rest of the items in order that there is neither gain nor loss in whole transaction, is (ax)/(1-a)%
Example 1: A medical store owner purchased medicines worth Rs. 6000 form a company. He sold 1/3 part of the medicine at 30% loss. On which gain he should sell his rest of the medicines, so that he has neither gain or loss?
Here a = 1/3 , x = 30 % Required gain % = (1/3*30)/(1-1/3) = 15 %
3. If cost price of 'a' articles is equal to the selling price of 'b' articles, then profit percentage =(a-b)*100/b
4. If a dishonest trader professes to sell his items at CP but uses false weight, then Gain %=Error*100/(True Value-Error) Gain%=(True weight-False weight)/(False weight) X100%
Example 2: A dishonest dealer professes to sell his goods at cost price but he uses a weight of 930 g for 1 kg weight. Find his gain per cent.
Gain % = 70*100/930
5.If a shopkeeper sells his goods at a% loss on cost price but uses b g instead of c g, then his profit or loss is [(100-a)(c/b)-100]% as sign positive or negative
Example 3:A dealer sells goods at 6% loss on cost price but uses 14 g instead of 16 g. What is his percentage profit or loss?
Here a = 20 , b = 40 Required answer = (40 -20)*100/(100- 40) = 33(1/3) %
6. If a dealer sells his goods at a% profit on cost price and uses b% less weight, then his percentage profit will be (b+a)/(100-b)X100%
7. If 'a' part of an article is sold at x% profit/loss, 'b' part at y% profit/loss and c part at z% profit/loss and finally there is a profit/lossof Rs.R, then Cost price of entire article =RS.(R*100)/(ax+by+cz)
Example 5: If 2/3 part of an article is sold at 30% profit, 1/4 part at 16% profit and remaining part at 12% profit and finally, there is a profit of Rs.75, then find the cost price of the article.
Here a = 2/3 , x = 30 % , b =1/4 , y = 16 % , z = 12 % and R = 75 Rs Required CP of article = (75*100)/(2/3*30+1/4*16+1/12*12) = 7500/25 = 300