Tips and Tracks for profit and 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.

Overhead Charges Such charges are the extra expenditures on purchased goods apart from actual cost price.

Such charges include freight charges, rent, salary of employees, repairing cost on purchased articles etc.

Note: If overhead charges are not specified in the question, then they are not considered

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 is incurred.

Question: 1    A man buys an article for Rs. 300 and sells it for Rs. 900. Find profit/loss.

Solution.        Here, SP > CP  Profit is earned.
According to the formula, Profit = SP - CP = 900 - 300 = Rs. 600

Question: 2    Raman purchased a car for Rs. 5 lakh and sold it for Rs 4 lakh. Find profit/loss in this transaction.

Solution.        Here, SP < CP Loss is incurred in this case.
According to the formula, Loss= CP- SP= (5-4) lakh=Rs. l lakh

Profit and Loss Tricks

As you have learned until now how to calculate profit as well as loss and also the percentage of them.
Now let us learn some tricks or formulas to solve maths problems based on gain and loss, starting from the general formulas.

1. Profit, P = SP – CP; SP>CP
2. Loss, L = CP – SP; CP>SP
3. P% = (P/CP) x 100
4. L% = (L/CP) x 100
5. SP = {(100 + P)/100} x CP
6. SP = {(100 – L)/100} x CP
7. CP = {100/(100 + P)} x SP
8. CP = {100/(100 – L)} x SP
9. 9.IF THE ARTICLE IS SOLD AT A GAIN OF SAY 35%, THEN
   SP =135% OF CP
10. IF AN ARTICLE IS SOLD AT A LOSS OF SAY 35%. THEN
    SP=65% OF C.P
11. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:
            
12. 
    
     

Type:1(Find Profit/Loss%)

Question:3  A person buys a toy for Rs. 50 and sells it for Rs.75. What will be his gain percent ?
Solution.   Given,CP=Rs. 50 and SP=Rs.75
         Profit = SP -CP = 75 - 50 = Rs. 25
         According to the formula,
         P% = (P/CP) x 100
         P%=25/50 x 100=50%
 

Question:4  A person buys a cycle for RS. 550 but because of certain urgency,he sells it for RS. 450. Find his loss percent.

Solution. Given, CP = RS. 550 and SP = RS. 450
Loss = CP-SP = 550 - 450 = RS.100
According to the formula,
L oss % = Loss/ CP*100%
= 100/550*100
= 18.18 %
 

Type:2(Find SP,CP)

Question:5  Find the SP, when CP is Rs 80 and gain is 20%.

Solution: CP = Rs. 80,
Gain percent = Rs. 20%
SP=120% of 80
SP=120/100 x 80
Thus SP is Rs. 96.

Question:6   A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.

Solution:  CP = [100 / (100 – Loss %)] * SP
Therefore, the cost price of the fan = (100/93)*465 = Rs. 500

Type:3

If A sold an article to B at a profit (loss) of r₁ % and B sold this article to C at a profit (loss) of r₂%,then

Cost price of article for C is given by cost Price for 

Question:7  Nikunj sold a machine to Sonia at a profit of 30%. Sonia sold this machine to Anu at a loss of 20%. If Nikunj paid Rs 5000 for this machine, then find the cost price of machine for Anu.    

Solution:1 Nikunj to sonia at 20% profit
               cp for nikunj= 5000

               Sp for nikunj=cp of sonia

                sp=30/100×5000+5000. (30% profit)

                  = 6500

Sonia to Anu

cp for Sonia= 6500

sp for sonia=cp of Anu

sp=6500-20/100×6500. (20% loss)

=Rs. 5200

Hence,cost price of machiene for Anu is Rs. 5200

Solution 2:
 CP for Anu= 5000x 130/100 x80/100=5200

Hence,cost price of machiene for Anu is 5200

 OR 
 by ratio method 

10  :  13  ( 30 % profit )
 5   :   4   ( 20 % loss)
----------
50   :   52 
-----------

50 unit = 5000 
1 unit = 100 
52 unit = 5200 
 

Type:4
By selling an item for Rs. x, a man losses L%. If he want to gain G% then
Selling Price will be=x(100+P)/100-L

Question:8  By selling a watch for Rs. 1440, a man losses 10%. At what price should he sell it to gain 5% ?
Solution 1:  Selling price of watch is S.P.=Rs.1440

Cost price of watch = 100−loss% / 100 ×S.P

∴ Cost price of watch =(100−10)/100×1440

∴ Cost price of watch =90/100×1440=Rs.1600

Selling price of watch to gain 5%=1600×1005+1600=80+1600=Rs.1680

Solution 2: 

  Sp= 1440x105/90=1680
Selling price of watch =Rs 1680

or

if an article is sold at 10 % loss then it was sold at 90% of its value 
90% of c.p = 1440 
1% of c.p = 1440/90 
1% of c.p = 16 

Now , if we want a profit of 5% i.e we have to sold the article at 105 % 
16 x 105 = 1680 rs . 


Type:5

If cost price of 'a' articles is equal to the selling price of 'b' articles, then

Profit %=                          

If it positive then profit otherwise loss

 
Question:9  The cp of 21 articles is equal to sp of 18 articles. find gain or loss %

Solution1: CP of 21 articles=x

CP of 1 article=x/21

SP of 18 articles=x

SP of 1 article=x/18

since x/21

gain=SP-CP

=x/18-x/21

=(7x-6x)/126

=x/126

gain%=gain/CP×100

=(x/126÷x/21)×100

=(x/126×21/x)×100

=100/6

=50/3

=16 2/3%

Solution 2:
Profit %=

           =(21-18)/18 x 100

            =1/6 x 100= 16 2/3%

OR 

21 c.p = 18 s.p 
c.p/s.p = 18/21 
it  means c.p : s.p = 6:7 

% profit = 1/6 x 100% = 16 2/3 % or 16.66 % 

Type:6 :
PROFIT = SELLING PRICE - COST PRICE 
LOSS = COST PRICE - SELLING PRICE 
 

Question:10   After selling 72 articles a man losses SP of 9 articles. Find loss % ? 

Solution: Let the S.P of one article = RS 1

S.P of 72 articles=72*1=72

Loss=9

C.P=72+9=81

Loss%  =  loss/CP x 100

=  9/81 x 100=11 1/9 %

OR 

loss = c.p - s.p 

9 s.p = 72 ( cp - s.p )

9 s.p  = 72 c.p - 72 s.p 

i.e -----72 c.p = 81 s.p 
c.p / s.p = 9 / 8 

loss = (1/9)  x 100 %  
11 1/9 % 

Question:11  After selling 72 articles a man earns a profit of SP of 9 articles. Find profit%.

Solution : Let the S.P of one article = RS 1

S.P of 72 articles=72*1=72

Profit=9

C.P=72-9=63

Profit %  =  Profit/CP x 100

=  9/63 x 100=14 2/7 %

OR 
profit = s.p - c.p

9 s.p = 72 ( s.p - c.p )
 

9 s.p = 72 s.p - 72 c.p 
or 
72 c.p = 63 s.p 
c.p : s.p = 7 : 8 

profit %  =  (1/7) x 100% = 14 2/7 % 

 

Type:7

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= a²/100 %

Question 12: A man sold 2 flats for Rs 675958 each.on one he gains 30% while on the other he losses 30%. How much does he gain/loss % in the whole transaction?

Solution:
            Loss%=30 x 30/100=9%