Profit and Loss With solved examples including shortcut methods

Profit and Loss

C.P = Cost price = the price at which an article is purchased. 

S.P = Sell price = the price at which an article is sold.

 

Formulae:

i.    Profit or Gain = S.P – C.P

ii.  Loss = C.P – S.P

iii.Profit % = (profit/ CP) × 100

iv. Loss % = (loss/CP) × 100

v.   Profit and loss are always counted on CP

vi. CP is always 100% in case of profit and loss

Observations

i. In case of profit or loss, the relation is generated between CP and SP.

IF 20% profit occurs on and article, it means

100% represent the cost price

90% represent the selling price

10% represent profit

i.e profit 20%     C.P 100%       % S.P 120%

ii. if 10% loss occurred in an article, it means:

  100% represents the cost price

  90% sell price

 10% represent the loss

Important points

i. When Cost price CP and profit or loss Percentage is given

Then CP = SP × (100 + profit) ÷ 100

CP = SP × (100 - Loss%)÷ 100

ii. When Sell price and profit or loss percentage is given

Then SP = CP × 100÷ (100 + profit%)

SP = CP × 100÷ (100 - Loss%)

iii. Marked price: MRP of an article is known as marked price or labeled price denoted by MP.

Discount

The reduction made on marked price is known as a discount

i.   Discount = MP – SP

ii.  Discount percentage = Discount ÷ MP × 100

iii. When the Marked price and the discount percentage is given then

SP = MP× (100- Discount %)÷100

iv.   Relation between CP and MP

MP = [CP× (100 ± profit& or Loss%)] ÷ (100- discount)

+ for profit, - For loss

Successive Discount

i. Discount equivalent to successive discounts of x% and y% of an article

  (x + y – XY ÷ 100) %

ii. Discount equivalent to successive discounts of x%, y%, and z%.

P = (x + y – xy ÷ 100) %

Equivalent discount of p and z  = (p + z – pz ÷ 100) %

Question-based on Profit and loss

Ex.1 A fruit seller makes a profit of 20% by selling mango at a certain price if the change 2Rs.. more for each mango then he can make a profit of 40%. Then find the CP of 1 mango.

Sol. Let Cost price of mango is 100

Then, 20% profit means sales price of mango is 120

Now 40% profit means Sales price of mango is 140

Now 2 Rs. more change profit from 120 to 140 

This means 2 = 20%

100% = 2 * (100/20) = 10 Rs. Ans.

Ex.2 A man purchased 2 fans for Rs. 1200 each and he sold one at 10% profit and the other he loses 5% then find the overall profit.

Sol. The cost price of fans is = 2400 Rs.

1200 Rs. + 1200 Rs.

1200 * 10/100) - 1200 *(5/100)

120 - 60 = 60 Rs. 

(60/2400) * 100 = 2.5% Ans.

Method 2 

If two articles both have same price then

(+profit% - loss%)/Number of articles

(10% - 5%)/2 = 2.5% Ans

Ex.3 If the cost price of an article is 1900 Rs. if 5/7 of its part is sold at a profit of 6% and remaining at a loss of 8%. then find its overall profit% or loss%.

Sol. If  articles are given in terms of part 5/7

The denominator gives the number of articles. thus the total number of articles is 7.

5 articles are sell at 6% profit and 2 articles are sell at 2% loss.

(+profit% - loss%)/Number of articles

(5*6% - 2*8%)/ 7 = 2% Ans

Ex.4 If the cost price of an article is 2500 Rs. if 2/3 of it is sold in the profit of 4% then in what % profit he sells the rest part to gain an overall 5% profit.

Sol. Let the total number of article is 3. 2 articles are sold at the profit of 4%. and 1 article is at x%

(2*4 + x)/3 = 5% Ans

Ex.5 By selling 32 orange for 30 Rs. A man losses 25% to gain 20% profit find the selling price of 4 orange.

Sol. 32 Orange = 30 Rs.

1 Orange =  30/32 Rs

4 Orange = (30/32) * 4 = 15/4

S.P %            S.P 

75%               15/4

120%             (15/4) * (120/75) 

75% = 15/4

1% = (15/4) *1/75

120% = (15/4)*120/75

= 6 Rs. Ans

Ex 6 A man sold 2 articles at the same price on first he gains 25% and the other he loses 20% then find it is his overall profit or loss percent.

Sol. If S.P is the same.

Method 1.

                        C.P1            S.P2

25% = 1/4       4                  5

20%=  1/5       5                  4 

In the above equation,

 equivalent fraction of 25% = 1/4 

In this case, 4 is cost price. in case of profit we add 1 with denominator to find S.P which is 5

In case of loss, we subtract 1 with the denominator. in the case of 20%, C.P is 5 and S.P is 4

Now we have to make a sale price equal. multiply the equation by 4 and 5

                        C.P1            S.P2

25% = 1/4       16                  20

20%=  1/5       25                  20  

C.P= 41            S.P = 40         loss =1

(1/41)*100 = 100/41 

Method 2

                       S.P1                   S.P2

                       125% C.P1        80% C.P2

CP1/CP2 = 16/25 

CP = 16+25= 41

Profit or loss =  16* (25/100) - 25 *(20/100) = -1

Loss = (1/41) * 100  = 100/41

Method 3

Formula = [100(P-L)- 2*P*L]/(100+P)+(100-L)

[100(25-20)- 2*25*20]/(100+25)+(100-20)

[100*5-2*25*20]/125+80

(500-1000)/205= 100/41Ans

Ex.7 A man sold 2 articles at the same price on first he gains 20% and in other he lost 20% then find the overall profit/Loss.

Sol. SP1 =  SP2

120 CP1 = 80 CP2

CP1/CP2= 80/120 = 2/3

CP is 2+3 = 5

Profit or loss = 2 *(20/100) - 3 *(20/100) = -1/5 loss

Loss = (-1/5) * (100/5) = 4%

Alternate formula when sale price is same = (r)²/100 =

(20)²/100 = 400/100 = 4% Ans

Ex.8 A man sells a book at a profit of 20% if he had purchased it 20% less and sold it 18 Rs. less then he has gained 25% find the cost price of the article.

Sol. method 1.

CP1 = 100%

SP1 = 120%

CP2 = 80%

SP2 = 80 * (125/100) = 100%

20% difference is in between SP1 and SP2

20% = 18 Rs.

100% = 18*(100/20) = 90 Ans

Method 2

                            CP1               SP1

20% = 1/5           5                      6

                           CP2                SP2

25%=1/4            4                      5

The difference between SP1 and SP2 is 1

1= 18

5= 90 RS. Ans

Ex.9 The profit earn by sold an article for 1920 Rs. is equal to the loss after selling the same article at 1280 Rs. then what price it should be sold to gain a 25% profit.

Sol. Profit = loss

SP - CP = CP - SP

1920-CP = CP - 1280

2CP = 3200

CP = 1600

100% = 1600

125% = 1600 *(125/100)

2000 Ans

Ex.10 If SP of 20 articles is equal to the CP of 25 articles find profit and loss percent.

Sol. 20 SP =  25 CP

SP/CP = 5/4

Profit = (1/4) * 100= 25% Ans

Ex.11 After selling 72 article man earn a profit of SP of 9 articles then find the profit.

Sol. P = SP - CP

9 SP = 72 SP - 72 CP

8 CP = 7 SP

SP/CP = 8/7 

1/7 = 14 ⅔ Ans