Profit And Loss - Arithmetic

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 %

(3) Loss = Sale Price (SP) – Cost Price (CP)

(4) Loss %

(5) Sale Price (SP)

(6) Sale Price (SP)

(7) Cost Price (CP)

(8) Cost Price (CP)

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 %

= 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 × 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%

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 × 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

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

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%

=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

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%

Thus, Loss %

Thus, loss = $5 and Loss % 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

Thus, loss = $5 and loss % % 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%

=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