 # Notes of Profit & Loss for Competitive Exam-III

Profit & Loss

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.

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 = 6 % , b = 14 g and c = 16 gRequired answer = [(100-6)(16/14)-100]% = 7(3/7) %

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%

Example 4: A dealer sells his goods at 20% loss on cost price but uses 40% less weight. What is his percentage profit  or loss?
Here a = 20 , b = 40
Required answer = (40 -20)*100/(100- 40) = 33(1/3) %

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