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Profit is the excess amount incurred in a business whereas loss is the deficit amount incurred. It is common to come across the terms such as Profit percentage, Loss Percentage, Selling Price, Cost Price, etc while buying any goods from a shop or even while discussing any financial terms. Cost Price is the cost incurred by a person while buying a good and Selling Price is the price of a good which is to be sold.
Also Read: How to Calculate Percentage
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Cost Price
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Cost Price is the cost incurred by a person while buying a good. Cost Price is an acronym for C.P. CP can also be thought of as the cost incurred by a consumer while buying any item from a shopkeeper or the cost incurred by the shopkeeper to buy the product from the manufacturer. Basically, the amount one has to pay for buying any good is called Cost Price. CP is one of the critical parameters to calculate the profit or loss of the article.
For example, while buying any item from the shop, say the price of the article is INR 20, then the cost to buy that item is INR 20 which will be your Cost Price.
The Formula for Cost Price is as follows:
- CP= SP - Profit
- CP=SP + Loss.
The video below explains this:
Profit and Loss Detailed Video Explanation:
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Selling Price
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Selling Price is the price of a good which is to be sold. Selling Price is an acronym for S.P. when a shopkeeper sells any good, he sells it at some price that is Selling Price. Basically, the amount one gets while selling any good is called Selling Price. SP is also one of the critical parameters to calculate the profit or loss of the article.
For example, if you go to a shop to buy any item and the shopkeeper prices it at a certain amount, say INR 50, so the INR 50 will be the selling price.
The Formula for Selling Price is as follows:
- SP= CP + Profit
- SP=CP – Loss.
Profit
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Profit is the positive difference between SP and CP. i.e., while buying any good, shop keeper keeps a profit margin on the item that profit margin is the extra amount he charges on the cost price is the profit or him. For example, the cost of making an article is INR 20 but while selling the article the shopkeeper sells it for INR 30. So, the profit of the shopkeeper is INR 30 – INR 20 i.e., INR 10.
- In Profit, The Selling Price is always greater than Cost Price i.e., SP>CP
- Profit = SP – CP.
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Loss
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Loss is the loss incurred by a person while selling a good. For example, if the cost of making an article is INR 50 but while selling, he has to sell it for INR 30. Therefore, the loss incurred by him will be INR 50 – INR 30 i.e., INR 20.
- In Loss, The Selling Price is always less than Cost Price i.e., CP>SP
- Loss = CP – SP.
Profit Percentage
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Profit percent is the percent gained after selling a good at a certain CP. It is always calculated over CP. For example, if a good is priced at INR 100 but is sold for INR 120 then the profit will be INR 20 and the Profit percentage will be 20/100 percent i.e., 20%.
- In Profit percentage, The Selling Price is always greater than Cost Price i.e., SP>CP
- Profit = SP – CP.
- Profit % = (SP-CP) / CP * 100
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Loss Percentage
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The percentage of loss incurred by a person in selling the good is the Loss percent. which is calculated keeping the CP as the base. For example, if the article is priced at INR 100 is sold for INR 75, there will be a loss as SP
- In Loss Percentage, The Selling Price is always less than Cost Price i.e., CP>SP
- Loss = CP – SP.
- Loss % = (CP-SP)/CP *100
From the above discussions, we can conclude that
- Profit percentage(P%) = (Profit /Cost Price) × 100
- S.P. = {(100 + P%)/100} × CP (if SP > CP)
- S.P. = {(100 – L%)/100} × CP (if SP < CP)
- C.P. = {100/ (100 + P%)} × SP (if SP > CP)
- C.P. = {100/ (100 – L%)} × SP (if SP < CP)
Where P% is Profit Percentage, L% is Loss Percentage, SP is Selling Price, and CP is Cost Price.
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Things to Remember
- SP is the Selling Price, defined as the cost of an item at which is sold
- CP is Cost Price when an item is bought the price at which it is bought is called Cost Price
- Profit is made when the Selling Price is larger than Cost Price. i.e., SP>CP
- Loss is incurred when Cost Price is Greater than Selling Price. i.e., SP
- Profit % and Loss % are always calculated on Cost Price.
- Profit = SP – CP.
- Loss = CP – SP.
- Profit % = (SP-CP) / CP * 100
- Loss % = (CP-SP)/CP *100.
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Sample Questions
Ques. Aman bought a pencil for INR 2 while the price listed by the shopkeeper was INR 3. Find the loss or gain made by Aman? (2 Marks)
Soln. As, Aman bought the Pencil at INR 2 and the shopkeeper listed it at INR 3 therefore, SP = 3, CP= 2
Hence, Aman Made a profit as he got a pencil at a cost less than that listed by the shopkeeper.
Hence, Profit = SP – CP
Profit = 3 – 2
Profit of INR 1 is made by Aman.
Ques. Determine the loss percentage if the CP of a commodity = INR 75 and SP = INR 50. (2 Marks)
Soln. Loss = CP - SP
= 75 − 50
= INR 25
Loss (%) = (Loss/CP) × 100
= (25/75) × 100
= 33.34%
Ques. A Shopkeeper sells a T.V. at a cost price of Rs 10000 with a profit of 25%. Calculate the price at which the Customer will purchase it. And also, find profit earned by the shopkeeper. (4 Marks)
Soln. C.P = Rs 10000
Profit % = 25%
Profit = C.P x profit %
Profit = 10000 X 25/100
Profit = Rs 2500
Selling price = Profit + C.P
= Rs 2500 + Rs 10,000 = Rs 12,500
So, the amount payable by the customer to the Shopkeeper = Rs 12,500
Ques. Find the cost price of an article that is sold for Rs. 270 at a loss of 10%. (2 Marks)
Soln. Here the S P = Rs. 270, also we have loss =10%. Let the C P = Rs x. Then the S P = 90% of the C P. Thus, we have:
270 = (90/100) × x. Simplifying this, we can see that x = 300.
Therefore, the cost price is = Rs. 300.
Ques. Anamika bought two air coolers at INR 15000INR 15000 each. She sold one at a profit of 15% and the other at a loss of 15%. Find if she made a profit or loss. (4 Marks)
Soln. Total cost price =INR 15000+INR 15000=INR 30000
Profit on air cooler is 15% of INR 15000= (15 * 15000) / 100=INR 2250
SP of one cooler =CP + Profit=INR (15000+2250) =INR 17250
Loss on the other cooler machine 15% of INR 15000= (15 * 15000) 15000=INR 2250
SP of the other cooler machine =CP–Loss=INR (15000–2250) =INR 12750
Total SP=INR (17250+12750) =INR 30000
So, Total CP =Total SP
Hence, Anamika neither makes profit nor loss.
Ques. A retailer bought eggs at INR 42 per dozen and sells 55 eggs for INR 20. Find his gain or loss percent. (5 Marks)
Soln. CP of 12 eggs =INR 42, therefore CP of 1 egg =INR 42/12=INR 7/2=INR 3.50 Therefore SP of 5 eggs =INR 20 and SP of 1 egg INR 20/5=INR 4
Profit on the sale of 1 egg =INR (4–3.50) =INR 0.50
Therefore,
Profit% =(Profit/CP) ×100%= (0.50/3.50) ×100%=100/7%=14(2/7) %
Hence, his profit percentage is 14(2/7) %
Ques. By selling a washing machine for INR 18858, a shopkeeper incurs a profit of INR 3592. Find his profit percent. (3 Marks)
Soln. SP of TV =INR 18858 and profit =INR 3592
Therefore, CP=SP–Profit=INR (18858–3592) =INR 15266
Thus, Profit%=(Profit×100)/CP
=(3592×100)/15266=23.52% (approx.)
Hence, his profit percent is 23.52% (approx.)
Ques. A fruit vendor bought 5 lemons for INR 5 and sold at the rate of 4 lemons for INR 5. Calculate:
(a) Profit in selling 60 lemons (3 Marks)
(b) Profit % (2 Marks)
Soln.
(a) CPCP of 5 lemons =INR 5
CP of 1 lemon =5/5=INR 1
CP of 60 lemons =1×60=INR 60
SP of 4 lemons =INR 5 hence, SP of 1 lemon =5/4
SPSP of 60 lemons = (5/4) ×60=INR 75
Profit =INR 75–INR 60=INR 15
Hence, the profit is =INR 15
(b) Profit%=(Profit/CP) ×100
= (15/60) ×100=25%
Hence, the profit percentage is 25%.
Ques. A manufacturer sold a dress for INR 720 and made a profit of 20%. Find the cost price of a dress. (4 Marks)
Soln.
Let the cost price of a dress be INR 100.
Profit was 20%.
So, the profit on 1 dress is INR 20 (because the CP is taken as INR 100).
Hence, the SP of 1 dress =INR 100+INR 20=INR 120
Let the actual cost price =INR x
Thus, 100: 120:x:720
⇒120×x=100×720
⇒x= (100×720)120=INR 600
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