Profit and Loss

All About Profit & Loss

PROFIT & LOSS
Profit and loss are determined by the value of cost price and selling price. Cost price is the price at which an article is purchased and selling price is the price at which article is sold
Profit = selling price - Cost price 

Loss = Cost price - Selling price 

Percentage profit and loss are always calculated on cost price. 

☞If a cost price of m articles is equal to the selling Price of n articles, then Profit percentage 

MARKED PRICE
Marked price is also known as the list price. It is the price which is marked on the article.

Where CP = cost price and MP = marked price

DISCOUNT
Shopkeepers devise several ways to attract customers (consumers). Sometimes they sell an article at a price lower than its list price (LP)/marked price (MP). Recall that reduction offered by retailer on the list price is called discount. We may recall that
Discount = MP - SP

Example 1: Marked price of a dining table is Rs 1350. It is sold at Rs. 1188 after allowing certain discount. Find the rate of discount.


Solution:
MP of the dining table = Rs. 1350
SP of the dining table = Rs. 1188
Discount allowed = Rs. (1350 - 1188) = Rs. 162
Discount percent =162/1350×100=12
This the rate of discount is 12%

As we had discussed the Multiplying Factor concept, it is very helpful to calculate the S.P. and C.P.
S.P. = C.P. × M.F.
In case of profit M.F. is greater then 1. 

If there is 10% profit, then
S.P. = C.P. × 1.1
M.F. = 1.1
For 15% profit M.F. = 1.5

Let’s take an example
If markup percentage is 30%, and the profit percentage is 17% then find the discount percentage.
Let  CP = 100
M.P. = 100 × 1.3 = 130
(M.P. – Marked up price)
S.P. = 100 × 1.17 = 117

Discount %
M.P. × Multiplying factor = S.P
130 × M.F. = 117
M.F = .9
Discount Percentage = 10%

In case of Loss   S.P < C.P And M.F. is smaller then 1.

Relation between multiplying factor of, Profit, Mark-up and discount

MF profit = MF mark-up × MF discount.

SUCCESSIVE DISCOUNTS
Sometimes more than one discount are offered by the shopkeeper on a single item or article. When two or more discounts are applicable successively to the list price of an article, they form the discount series.
Suppose a shopkeeper is offering 3 successive discounts of 10%, 20% and 30% then to calculate effective discount we assume that marked price is 100, then final value becomes 0.90 × 0.80 × 0.70 × 100 = 0.54 × 100 = 50.4
Total discount = 49.6%.

☞When there  are two successive Profit of x % and y % then the resultant profit  per cent is given by 

☞If there is a Profit of  x% and loss of  y %  in a transaction, then the  resultant profit or loss% is given by 

Note-  For profit use sign + in previous formula and for loss use – sign.
if resultant come + then there will be overall profit, if it come – then  there will be overall loss.

Example 2:
If two articles are sold at same selling price one at 30% profit another at 30% loss then what is his overall percentage profit or loss?

FALSE WEIGHT PROBLEMS
Shown or indicate weight is always equivalent to selling price, and actual/true weight is equivalent to cost price.

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

Example 3:
A shopkeeper takes 20%, extra quantity while purchasing the milk, and gives 25% less than the indicated weight while selling the milk. Find the profit percentage of he sells at the cost price only. 

Solution: 
Suppose the price of milk = 1 Rs per ml shopkeeper takes 120 ml, and pays only Rs. 100
While selling he gives only 75 ml and shows 100 ml.
Total selling price of 120 ml
 100/75×120 = 160, hence percentage profit = 60% 

Profit and Loss

Q.1 Loss on selling on object for Rs. 500 is equal to the profit gained if the object is sold for Rs.900. Find the original C.P. of the object.

If we are given two selling prices of which one is showing loss and other giving the profit, find out the difference and divide it in the ratio of loss and profit. Here the ratio was 1 : 1, so we divided 400 in 1 : 1


Q.2 A shopkeeper when sells on object for Rs. 900, then he faces loss which is equal to half of the profit gained if the object is sold for Rs. 1200.  Find cost price.


C.P. = 900+100  or  1200 - 200

    =Rs 1000

In this question, the ratio of loss and profit was 1 : 2 so, accordingly we divided the difference in the ratio 1 : 2 which gave us 100 and 200.

Q.3 A person gained Rs.50 more as profit from the amount he lost if he had sold it for Rs. 600, after selling it for Rs. 760. Find C.P.



C.P  = 600 + 55 or   760 -105
=Rs. 655

Profit on 2nd S.P. will be Rs. 50 more than the loss on 1st S.P., So if we deduct Rs. 50 from difference, the remaining will be equal profit and loss so, either add 55 to 1st S.P. or deduct 105 from 2nd S.P.

Q.4 A shopkeeper sells an article at 20% profit. Had he purchased it at 10% less price and sold it at 30% profit, he would have charged Rs. 15 less for the article. Find original C.P. of the article.

∴ Actual C.P. = 100 x  5 = Rs. 500

We assume the C.P. = Rs. 100 and S.P. = Rs.120. (After 20% profit).  After purchasing it for 10% less, the new C.P. becomes 90 and selling it at 30% profit gives now S.P. = Rs. 117. Difference is Rs. 15 which is 5 times of obtain difference. Original C.P. will also be 5 times of assumed C.P. = Rs.500

Q.5 A reduction of 20% in the cost price of sugar enables a house wife to buy 5kg. more sugar for Rs. 100. Find original cost price.

 Original Price = 100/20  =Rs.51 Kg

20% can be written as 1/5. So, if the original price was 5, new price will be for. In the same way,old consumption will be 4 unit and new consumption will be 5 unit because decrease in price of the sugar will be directly proportional to the increase in consumption increase in consumption is 1 unit but actual increase is 5 Kg. 
 ∴ Original consumption and new consumtion will also be 5 times i.e. 20 kg and 25 kg.

Some questions based on above concepts:-

1.1/3’rd of a commodity is sold at 15% profit, ¼ is sold at 20% profit and the rest at 24% profit. If the Total profit is Rs. 80 is earned then find the value of commodity?

A) 350

B) 410

C) 400

D) 300

2.A man purchases a certain no. of apple at 5 per rupee and same no. at 4 per rupee. He mixes them together and sells them at 4 per rupee. What is  his gain or loss%?

A)  Gain 20 %

B)  Gain 11.11%

C) Loss 11.11%

D)  Loss 20 %

3.A trader allows a Discount of 5% for cash payment. How much approx % above cost price must he mark his goods to make a profit of 10%?

A) 8.9% 

B) 10%

C) 12.75%

D) 15.8%

4.If selling price is doubled, the profit triples. Find the profit percent?

A) 100%

B) 116.67%

C) 200%

D) 300%

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

A) 2200

B) 2400

C) 2500

D) 2000

6.Abhishek purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

A) 5.4

B) 5.6

C) 6.5

D) 4.5

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

A) 33.33%

B) 66.66%

C) 44%

D) 50%

8.On selling 17 toys at Rs. 720, there is a loss equal to the cost price of 5 toys . The cost price of a Toy is:

A) Rs. 50

B) Rs. 60 

C) Rs. 65

D) Rs. 70

9.A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are Sufficent?

I. Sale price of the article

II. Number of articles sold

A)Only I is sufficient.

B)Only II is sufficient.

C)Both I & II are sufficient.

D)Either I or II are sufficient.

E)Both I & II are not sufficient.

10.A man purchases 10 Cows at Rs. 3000 each. 1 Cow died. He sold 2 Cows at 5% loss, at what rate he should sale the remaining Cows, so as to gain a Profit of 10 % on the total Cost?

A) Rs.4000

B) Rs.3000 

C) Rs.3900

D) Rs. 4500

E) Rs. 4200

Answers:-

1). C

2). B

3). D

4). A

5). D

6). B

7). C

8). B

9). C

10). C

Important Tricks and Quiz on Profit and Loss

Important Tricks and Quiz on Profit and Loss

Hello Readers,

Below in the post ,We shall discuss about Profit and Loss of the Quant section.  Now a days these topics  have became an important part of the Quant test ,So Here we will help you in this.We will  provide short tricks and quant quiz.

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

Tricks and concepts on Profit and Loss