Profit and Loss

Profit and Loss

Important Formula:

1. Profit = SP-CP

2. Loss  = CP-SP

3. Profit% = (Profit/ CP)*100

4.Loss % = ( Loss/CP)*100

5. For Dishonest shopkeeper :

% profit or % loss = (Error *100) / True Value

6. SP= MARKED PRICE - DISCOUNT
[ Whenever discount is given , it is given on Marked Price, hence in such case Marked Price should be treated as 100%]

Important  Points : 

1.Always consider CP as 100% and then solve the question. Try to use all the variables in percentage form only.
2. CP should be the base value for calculating  Profit or Loss .

3. For   Successive Discount:

Net Discount =  a+ b -(ab/100)

4. When CP1 = CP2 and profit% 1st = Loss% on 2nd,
then : NO PROFIT & NO LOSS in overall transaction.

5. When SP1 = SP2 and profit% 1st = Loss% on 2nd,
then : LOSS in overall transaction.
Loss% = (rate*rate)/100

Solved Examples 

Q1. A man sold a book at 480 Rs and he gained 20%. Find CP ?

Solution: 

CP =  100% and SP= 120%

Here,

120% = 480

100% = x (i.e. CP)

Use cross multiplication and solve further,

x = 400

Q2.

If  Mark Price of a TV set  is 20% more than its CP. Shopkeeper  gives discount of 5%. Find profit% ?

Solution:

CP = 100%

MP= 120%

SP = 120% - ( 5% of 120%)  = 120% - 6%  = 114%

Profit% = 114% - 100% = 14%. 

Q3. 

If CP is 96 % of SP. Find Profit %?

Solution: 

Given that, CP= 96%  and SP = 100% 

profit = SP-CP = 100% - 96%  = 4% 

Profit% = (Profit/ CP)*100  = (4%/ 96%)*100   =  400/96 = 4.16 .

Q4. A Boy bought a bag with 15% discount on labelled price. He sold the bag for Rs 2880 with 20% profit on labelled price. At which price did he bought the bag?

Solution: 

CP of bag = 100% of labelled price - 15%  = 85% of   labelled price is CP

120 % of labelled Price  =  2880

85% of   labelled price   =  x ( i.e. CP)

Use cross multiplication and solve further,

x = (2880*85%)/ 120%  = Rs 2040.

Q5. A customer gets 2  discount of 40% and 20% . This discount is equivalent to how much  discount?

solution:

Net Discount =  a+ b -(ab/100)

Net discount = 40+20 - (40*20/100) = 60-8 = 52%.

alternate method:

100  - (40% of 100) - ( 20% of 40% of 100) 

100-40-8 = 52% 

Q6. A shopkeeper give 2 successive discount  of 20% and 15 % on purchase of an article. Ia a boy pays Rs 1156 for that article then find the Marked price ?

solution

Net Discount =  a+ b -(ab/100)

                      = 20+15- (20*15/ 100)  =  35-3 = 32%

It means the Boy has paid 68 %  [ as he get 32% discount]

now, 

68% = 1156

100%  = x ( i.e. marked price)

x = 1156*100 / 68 = Rs 1700.

Q7. A shopkeeper sell his good at CP., but he uses a weight of 960 gram instead of 1kg . Find his profit % ?

solution:

% profit  = (Error *100) / True Value 

               =(40 *100)/960 = 4000/960 = 4.16.

Q8. A man purchases some lemon at 6 lemon per 5 Rs. and sell all the lemon at 4 lemon per 3 Rs.

      Find Profit or loss % ?

solution:

              Quantity      Price

CP             6                5

SP              4                3

Please note , the TRICK is cross multiplication  we will use SP as  6*3 [ from left top to right bottom]   and CP  as 4*5  [ from left bottom  to right top ] 

SP = 18

CP =  20

loss = 2

loss % = 2*100/20   = 2% loss.

Q9. A person bought two articles for the same price and sold them at a profit of 10% on one and a loss of 10% on the other. What is the overall profit or loss % made by him?

here,
 CP1= CP2
 PROFIT% = LOSS % = 10%
When CP1 = CP2 and profit% on 1st = Loss% on 2nd,
then : NO PROFIT &NO LOSS in overall transaction.

Q10.If a person sold two articles at same price and realized 10% profit on one and 10% loss on the other article. What net profit/loss % does he make?
here,

 SP1= SP2
 PROFIT% = LOSS % = 10%
LOSS in overall transaction.
Loss% = (rate*rate)/100 = (10*10)/100 = 1%.

Q11.A shopkeeper marks his goods in such a way that after allowing a discount of 10%, he gains 17%. How much percent above C.P. is the marked price?

Solve it using ,
Net percentage change =  a+ b -(ab/100)

profit% = % change in MP (a)+ discount% (b)- ab/100
17  = a-10-(10a/100)
1700  = 100a-1000-10a
1700+1000 = 100a-10a
2700= 90a
a= 30
Marked price is 30% more than CP.