profit and loss formulas

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TRICKS  FOR SOLVING QUESTIONS RELATED TO PROFIT AND LOSS:

COST PRICE : The price at which an article is purchased is called its cost price (C.P.)

SELLING PRICE : The price at which the article is sold is called its selling price (S.P.)

1. If the cost price (C.P.) of the article is equal to the selling price (S.P.), then there is no loss or gain.

2. If the selling price (S.P.) > cost price (C.P.), then the seller is said to have a profit or gain,

Gain/Profit = S.P. - C.P.

3. If the cost price (C.P.) > selling price (S.P.), then the seller is said to have a loss,

Loss = C.P. - S.P.

4.  Gain% = {(Gain*100)/C.P.}

5. Loss% ={(Loss*100)/C.P.}

6. S.P. = {(100+Gain%)/100 * C.P.}

7. S.P. = {(100 - Loss%)/100 * C.P.}

8. C.P. = {(100/(100+Gain%) * S.P.}

9.C.P. = {(100/(100 - Loss%) * S.P.}

10. If an article is sold at a profit/gain of 30%, then S.P. = 130% of the C.P.

11. If an article is sold at a loss of 20%, then S.P. = 80% of the C.P.

12. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then in this transaction the seller always incurs a loss given by: 

                        {x^2/100}%

13. A single discount equivalent to discount series of x% and y% given by the seller is equal to 

                                   {x +y - xy/100}%

14. If a trader professes to sell his goods at cost price, but uses false weights, then 

Gain% = {Error/(True value - Error) x 100}%

 1. How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?

A.  60%

B.  55%

C.  70%

D.  50%

2. A dishonest dealer professes to sell his goods at the cost price but uses a false weight of 850 g instead of 1 kg. His gain percent is

A.  71 11/17%

B.  11 11/17%

C.  17 12/17%

D.  17 11/17%

3. An article is sold at 10% loss. If the selling price is Rs. 40 more, there will be a gain of 15%. The cost price of the article is:

A.  Rs. 140

B.  Rs. 120

C.  Rs. 175

D.  Rs. 160

4. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, find out the value of x

A. 15

B. 25

C. 18

D. 16

5.In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A. 30%

B. 70%

C. 100%

D. 250%

6.The percentage profit earned by selling an item for Rs. 1920 is equal to the percentage loss incurred by selling the same item for Rs. 1280. At what price should the item be sold to make 25% profit?

A. Insufficient Data

B. Rs. 3000

C. Rs. 2000

D. Rs. 2200

7. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:

A. 30%

B. 33 1/3%

C. 35%

D. 44%

8. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:

A. 14 2/7% gain

B. 15% gain

C. 14 2/7 % loss

D. 15 % loss

9.A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. What is his profit percentage?

A. 6%

B. 5%

C. 4%

D. 7%

10. A trader gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the labeled price of an item. The final sale price of the item is Rs.704. Find out the labeled price?

A. 1000

B. 2000

C. 1200

D. 920

ANSWER AND SOLUTION :

1(A)Explanation :
Let cost price of goods be Rs 100.
Gain = 20%
Therefore, Selling price = Rs 120
Discount = 25%
Marked Price = (100/100-25)x120
= Rs. 160
i .e.  60% more

2(D)Explanation :
If a trader professes to sell his goods at cost price, but uses false weights, then
Gain% = {Error/(True value - Error) x 100}%
In the given question, Error = 1000 - 850 = 150
Thus, Gain% = {150/(1000 - 150) x 100}%
= 17 11/17%

3(D)Explanation :
Let the cost price be Rs. x.
Selling Price at 10% loss = 90x/100
Selling Price at 15% gain = 115x/100
Thus, according to the problem,
115x/100 - 90x/100 = 40
x = Rs.160

4(D)Explanation :
Let the Cost Price (CP) of one article = 1
=> CP of x articles = x ------------------------------(Equation 1)
CP of 20 articles = 20
Given that cost price of 20 articles is the same as the selling price of x articles
=> Selling price (SP) of x articles = 20--------------(Equation 2)
Given that Profit = 25%
(SP-CP/CP)=25/100=1/4------------( Equation 3)
Substituting equations 1 and 2 in equation 3,
(20-x)/x=1/4
80-4x=x
5x=80
x=80/5=16

5(B)Explanation:
 Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
 Required percentage = (295/420 x 100)% = 1475/21 % = 70% (approximately).

6(C)Explanation :
Let CP = x
Percentage profit earned by selling an item for Rs. 1920
= (SP-CP/CP0 ×100
=(1920-x)/x×100
Percentage loss incurred by selling the same item for Rs. 1280
= (CP-SP)/CP×100
= (x-1280)/x ×100
Given that Percentage profit earned by selling an item for Rs. 1920=Percentage loss incurred by selling the same item for Rs. 1280
(1920-x)/x ×100 = x-1280/x ×100
(1920-x)/x = (x-1280)/x
1920–x = x–1280
2x=1920+1280=3200
x=3200/2
=1600
Required Selling Price = CP×125/100
=1600×125/100 =1600×5/4
=400×5=2000

7(D)Explanation:
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.(5/6 x 30) = Rs. 25.
S.P. of 30 articles = Rs.(6/5 x 30) = Rs. 36.
 Gain % =  (11/25 x 100) % = 44%.

8(A)Explanation:
C.P. of 1 orange = Rs.(350/100) = Rs. 3.50
S.P. of 1 orange = Rs (48/12) = Rs. 4
 Gain% = (0.50/3.50  x 100) %  = 100/7 % = 14 2/7%

9(B)Explanation :
CP of 1st variety rice=20
CP of 2nd variety rice=36
CP of the 56 kg rice mixture=(26×20+30×36)=520+1080=1600
SP of the 1 kg rice mixture=30
SP of the 56 kg rice mixture=30×56=1680
Gain=SP-CP=1680-1600=80
Gain%=Gain/CP×100=80/1600×100=100/20=5%

10(A)Explanation :
Let the labeled price=x
SP=704
Initial Discount=20%
Price after initial discount=x×80/100
Additional discount=12%
Price after additional discount=x×80/100 × 88/100
But Price after additional discount=SP=704
=> x×80/100 × 88100=704
=>x×4/5 × 22/25=704
=>x=704×25/22 × 5/4=176×25/22×5
=8×25×5=40×25=1000