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Profit Generation

The purpose of studying Profit, Loss and Discount is to understand the mechanism of profit generation under different situations. Broadly it can be seen in two ways:

Honest Ways

Questions which you will find here will be based either in terms of Rs or in terms of goods.

Type 1: Questions in terms of goods
 
In these types of questions, CP of a fixed number of goods are compared with the SP of another field number of goods. Let us see through an example:
 
Example-1
The CP of 30 articles is equal to the SP of 40 articles. What is the profit or loss percentage?
Solution
To obtain the same amount of money, which was needed to purchase 30 articles, we need to sell 40 articles, which is more than what we have got for the same sum.
 
It means we need to arrange 10 more articles apart from the articles which we have purchased. So, there will be a loss.
 
Now, CP of 30 articles = SP of 40 articles
Or, CP/SP = 30/40 = ¾
Or, 1 – CP/SP = 1− ¾ = ¼
So, Loss percentage
= (1 – CP/SP) × 100 = ¼ × 100 = 25%
 
Alternatively,
CP of 30 articles = SP of 40 articles
= Rs 120 (Assume)
So, CP of one article = Rs 4
SP of one article = Rs 3
Obviously, there is a loss of Re 1
Loss percentage = ¼ × 100 = 25%
Or, Otherwise we can use Profit/loss Percentage
Description: 2254.png
 

Type 2: Questions in terms of money
 
Basically questions in terms of money relate to the CP or SP. However, sometimes the results given below also come handy in solving problems.

Some Important Results
 
When SPs of two articles are same
  1. First one is sold at a profit of x% and second one is sold at a profit of y%.
     
    Ratio of CP1:CP2 = (100 + y):(100 + x)
  2. First one is sold at a profit of x% and second one is sold at a loss of y%.
     
    Ratio of CP1:CP2 = (100  y):(100 + x)
  3. First one is sold at a loss of x% and second one is sold at a loss of y%.
     
    Ratio of CP1:CP2 = (100  y):(100  x)
  4. First one is sold at a loss of x% and second one is sold at a profit of y%.
     
    Ratio of CP1:CP2 = (100 + y):(100  x)
Example-2
SPs of two articles are same. One is sold at a loss of 20% and another one at a profit of 20%. What is the net loss/profit in the whole transaction?
Solution
Assume that SPs of each of the article = Rs 100
So, CP1 (For the article which is sold at a loss of 20%) = 100/0.8 = Rs 125
CP2 (For the article which is sold at a profit of 20%) = 100/1.2 = Rs 83.33
So, net CP = Rs 125 + Rs 83.33 = Rs 208.33
As we can observe now that SP<CP, so, there is a loss.
Loss % = (8.33/208.33) × 100 = (1/25) × 100 = 4%
 
Alternatively, if SPs of two articles are same, and one is sold at a profit of x% and another is sold at a loss of x%, then in that case there will be a loss always. And loss percentage = Description: 2263.png%
 

Example-3
Two articles are sold at Rs 12,000 each. One is sold at a profit of 20% and another one at a loss of 20%. What is the net loss?
Solution
SP1 = Rs 12,000
CP1 = Rs 12,000/ 1.2 = Rs 10,000
SP2 = Rs 12,000
CP2 = Rs 12,000/ 0.8 = Rs 15,000
So, total CP = Rs 25,000 and total SP = Rs 24,000
So, loss = Rs 1,000.
Alternatively, since there is a loss of 4%. So, for every Rs 100 invested, Rs 96 is coming back and Rs 4 is lost. In our case, 96% = Rs 24,000; so, 4% = Rs 1,000.
 

Example-4
Due North Inc. is the number 1 idea developer company worldwide. One day, they sold Idea 1 to CL and Idea 2 to AMS at a profit percentage of 20% and 30%, respectively. If the sum of developing Idea 1 and Idea 2 is Rs 25,000, what is the developing cost of Idea 1?
Solution
The ratio of developing cost of Idea 1 and Idea 2 = 130:120
 
So, developing the cost of Idea 1 = Description: 2272.png × 25,000 = Rs 13,000
 

Dishonest Ways

Dishonest ways of earning profit includes adulterating or using faulty balance or both of these simultaneously.
 
Example-5
A shopkeeper sells his articles at his CP but uses a faulty balance which reads 1000 gm for 800 gm. What is his actual profit percentage?
Solution
This question can be solved in several methods.

Method 1 Shopkeeper’s net profit = 200 gm
CP of 1000 gm = SP of 800 gm
So, profit % = 200/800 × 100 = 25%

Method 2 Since while selling, 800 g = 1 kg
So, 200 gms = 1/4 kg
So, profit = 1/4 = 25%

Method 3 While selling, since the shopkeeper is branding 800 grams as 1 kg, so 1000 grams will be branded as 1000/800 = 1.25 kg and while purchasing, he has paid for just 1000 grams.
So, net profit = (1.25 – 1) = 0.25 kg
So, profit percentage = 0.25/1 × 100 = 25%
 
 
Example-6
A shopkeeper marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000 gm for 800 gm. What is his net profit percentage?
Solution
Let us assume his CP/1000 gm = Rs 100
So, his SP/kg (800 gm) = Rs 126
So, his CP/800 gm = Rs 80
So, profit = Rs 46
So, profit percentage = 46/80 × 100 = 57.5%
 

Some more examples

Example-1
A cloth store is offering “Buy 3, get 1 free.” What is the net percentage discount being offered by the store?
Solution
Suppose price of one article is Re 1. So, price of 4 articles = Rs 4. Now the whole scene can be understood as – We are paying only Rs 3 at the place of Rs 4. So, discount = Re 1. So, discount percentage = ¼ (discount/total price) = 25%
 
 
Example-2
A shopkeeper sells his goods at its CP only. But still he manages to gain a profit of 40% because he has manipulated his weights. Find how many grams he is actually selling at the place of 1000 gm.
Solution
To earn a profit of 40%, shopkeeper needs to make 1.4 kg out of 1 kg. So, he will be sellingDescription: 2281.png grams = 728 grams at the place of 1 kg. 
 
 
Example-3
When an article is sold at 20% discount, SP is Rs 24. What will be SP when the discount is 30%?
Solution
20% discount = 0.8 of MP = Rs 24
So, MP = Rs 30
So, SP when discount is 30% = Rs 21
 




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