Profit And Loss
Important Facts and Formulas
Cost Price (CP) : Cost Price is the price at which an article is purchased. C.P. is the abbreviation generally used for cost price.
Example: If an article is purchased at $40.00, then the cost price of this article (CP) = $40.00
Sale Price or Selling Price (SP): Sale price is the price at which an article is sold. S.P. is the abbreviation used for sale price. Sell price is called selling price also.
Example: If a book is purchased at a price of $10.00 and sold for $20.00, then here
Cost price (CP) = $10.00 and Sale price or selling price (SP) = $20.00
Profit: When an article is sold at more than cost price, it is said that seller earned a profit.
This means when Cost Price (CP) > Sale price or Selling Price (SP), then it is profit.
Profit is called gain also.
Example: The cost price of a pen is $20.00 and it is sold at $25.00.
Cost price (CP) = $20.00 and Sale Price (SP) = $25.00
Clearly, Cost price (CP) < Sale Price (SP)
Thus, seller is in profit or gain.
Loss: When an article is sold at less than the cost price, the deal is called in Loss .
This means when Cost Price (CP) > Sale Price (SP), then it is called Loss
Example: Let a cycle is purchased at $100.00 and sold at $90.00. Here seller is in loss.
Here, Cost Price (CP) = $100.00 and Sale Price (SP) = $90.00
Clearly Cost Price (CP) > Sale Price (SP)
Thus, it is a deal of Loss.
Important Formula to Calculate Profit and Loss
(1) Loss or Gain is always calculated on cost price
(1) Gain Or Profit = Sale Price (SP) – Cost Price (CP)
(2) Gain % `=(text{Gain} xx 100)/(text(C.P.)`
(3) Loss = Sale Price (SP) – Cost Price (CP)
(4) Loss % `=(text{Loss} xx 100)/(text(C.P.)`
(5) Sale Price (SP) `=(text{100 + Gain%})/100xxC.P.`
(6) Sale Price (SP) `=(text{100 - Loss%})/100xxC.P.`
(7) Cost Price (CP) `=100/(text{100 + Gain%})xxSP`
(8) Cost Price (CP) `=100/(text{100 - Loss%})xxSP`
Questions Based on Profit And Loss
Question (1) The cost price of a pen is $10.00 and sale price is equal to $15.00. Find the profit or loss percent.
Solution:
Given, Cost Price (CP) = $10.00
And, Sale Price or Selling price (SP) = $15.00
Since, here sale price (SP) is greater than Cost Price, thus it is a profit.
Thus, Profit% = ?
Calculation of Gain or profit
We know that, Profit = Sale Price (SP) – Cost Price (CP)
= 15.00 – 10.00 = 5.00
Thus, Profit = $5.00
Calculation of Gain or profit %
We know that,
Thus, profit % `=(5xx100)/10`
= 50%
Thus, profit% = 50% Answer
Alternate Method
Here, cost price (CP) = $10.00
And sale price (SP) = $15.00
Calculation of Gain or profit
Thus, profit = SP – CP
= 15.00 – 10.00 = 5
Thus, profit = $5.00
Calculation of Gain or profit %
∵ In the cost price of $10.00 profit = $5.00
∴ In the cost price of $1, profit `=5/10`
∴ In the CP of $100, profit `=5/10xx100`
= 5 × 10 = 50%
Thus, profit % = 50% Answer
Question (2) If a pen is purchased at $50.00 and sold at $55.00, then find the profit percentage?
Answer
Given, Cost price (CP) = $50.00
And, Sale Price (SP) = $55.00
Therefore, profit % =?
Calculation of Gain or profit
Profit = Sale price (SP) – Cost price (CP)
= 50.00 – 55.00 = 5.00
Thus, profit = $5.00
Calculation of Gain or profit %
We know that,
Thus, profit% `=(5xx100)/50 = 10%`
Thus, profit % = 10% Answer
Alternate Method
Here, cost price (CP) = $50.00
And sale price (SP) = $55.00
Calculation of Gain or profit
Thus, profit = SP – CP
= 55.00 – 50.00 = 5
Thus, profit = $5.00
Calculation of Gain or profit %
∵ In the cost price of $50.00 profit = $5.00
∴ In the cost price of $1, profit `=5/50`
∴ In the CP of $100, profit `=5/50xx100`
= 5 × 2 = 10%
Thus, profit % = 10% Answer
Question (3) The sale price of a book is $250.00. If this book was purchased at $200.00, find the percentage of profit.
Solution:
Given, Cost price (CP) = $200
And, Sale price (SP) = $250
Thus, profit % = ?
Calculation of Gain or profit
Profit = Sale price (SP) – Cost price (CP)
= 250 – 200 = 50
Thus, profit = $50
Calculation of Gain or profit %
Now, we know that,
Thus, Gain `=(50xx100)/200`
`=50/2=25%`
Thus, profit % = 25% Answer
Alternate Method
Given, Cost price (CP) = $200
And, Sale price (SP) = $250
Thus, profit % = ?
Calculation of Gain or profit
Profit = Sale price (SP) – Cost price (CP)
= 250 – 200 = 50
Thus, profit = $50
Calculation of Gain or profit %
∵ In the cost price of $200.00 profit = $50.00
∴ In the cost price of $1, profit `=50/200`
∴ In the CP of $100, profit `=50/200xx100`
`=50/2=25%`
Thus, profit % = 25% Answer
Question (4) The cost price of a bicycle is $250. If it is sold for $200, then find the loss and loss percent.
Solution:
Here, given, cost price (CP) = $250
And, sale price (SP) = $200
Therefore, loss and loss % = ?
Calculation of Loss
Loss = Cost price (CP) – Sale price (SP)
= 250 – 200 = 50
Thus, Loss = $50
Calculation of Loss %
Now, we know that,
Thus, loss% `=(50xx100)/250`
`=100/5` =20%
Thus, loss % = 20%
Thus, loss = $50 and loss% = 20% Answer
Alternate Method
Here, given, cost price (CP) = $250
And, sale price (SP) = $200
Therefore, loss and loss % = ?
Calculation of Loss
Loss = Cost price (CP) – Sale price (SP)
= 250 – 200 = 50
Thus, Loss = $50
Calculation of Loss %
∵ In the cost price of $250.00 loss = $50.00
∴ In the cost price of $1, loss `=50/250 =1/5`
∴ In the CP of $100, loss `=1/5xx100 =20%`
Thus, loss = $50 and loss % = 20% Answer
Question (5) A pen is sold at $15. If the cost price of pen is $10, then find the loss and loss% on selling on pen?
Answer
Here, given, Sale price (SP) = $10
And, Cost price (CP) = $15
Thus, loss and loss% = ?
Calculation of Loss
We know that, Loss = Cost price (CP) – Sale price (SP)
= $15 – $10 = $5
Thus, Loss = $5
Calculation of Loss %
Now, we know that,
Thus, Loss% `=(5xx100)/15`
`=100/3=33\1/3%`
Thus, Loss % `=33\1/3%`
Thus, loss = $5 and Loss % `=33\1/3` Answer
Alternate Method
Here, given, Sale price (SP) = $10
And, Cost price (CP) = $15
Thus, loss and loss% = ?
Calculation of Loss
We know that, Loss = Cost price (CP) – Sale price (SP)
= $15 – $10 = $5
Thus, Loss = $5
Calculation of Loss %
∵ In the cost price of $15.00 loss = $5.00
∴ In the cost price of $1, loss `=5/15 =1/3`
∴ In the CP of $100, loss `=1/3xx100 =3\1/3%`
Thus, loss = $5 and loss % `=3\1/3` % Answer
Question (6) A trader purchase rice at the rate of $0.4 per kg and sold it for $0.3 per kg. If he purchased 100kg of rice, find the loss and loss percentage.
Solution:
Quantity of rice purchased = 100 kg
Given, cost price per kg = $0.4
Thus, total cost price = 0.4 × 100 = $40
And sale price per kg = $0.3
Thus, total sale price = $0.3 × 100 = $30
Now, we know that,
Calculation of Loss
Loss = Cost Price (CP) – Sale Price (SP)
= $40 – $30 = $10
Thus, Loss = $10
And we know that
Calculation of Loss %
Thus, Loss% `=(10xx100)/40`
`=100/4 =25%`
Thus, Loss = $10 and Loss % = 25% Answer
Alternate Method
Quantity of rice purchased = 100 kg
Given, cost price per kg = $0.4
Thus, total cost price = 0.4 × 100 = $40
And sale price per kg = $0.3
Thus, total sale price = $0.3 × 100 = $30
Calculation of Loss
Now, we know that,
Loss = Cost Price (CP) – Sale Price (SP)
= $40 – $30 = $10
Thus, Loss = $10
Calculation of Loss %
∵ In the cost price of $40, the loss = $10
∴ In the cost price of 1, the loss `=10/40=1/4`
∴ In the cost price of 100, the loss `=1/4xx100=25`
Thus, loss % = 25%
Thus, Loss = $10 and Loss % = 25% Answer
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