Profit And Loss
To make profit is the basic aim of any business.
Cost Price: It is the price at which any article or unit or item is bought. It is abbreviated as CP.
Selling Price: It is the price at which any article or unit or item is sold. It is abbreviated as SP.
Profit: If Selling Price is greater than Cost Price then seller makes profit.
Profit = SP – CP
Loss: If Cost Price is greater than Selling Price then seller incurs loss.
Loss = CP – SP
One point is to be noted that loss or profit is always calculated with reference to CP.
Shortcut Method For Profit And Loss
Example 1:
By selling goods for $9000; a profit of $1000 is made. Find the profit percent.
Solution:
Given, selling price of goods = $9000 and profit made = $1000
Therefore, C.P. = S.P. - profit
= $9000 - $1000
= $8000
And, profit% = (profit/cost price) × 100%
= (1000/8000) × 100%
= (1/8) × 100%
= 12.5%
Therefore, profit percent by selling goods is 12.5%.
Example 2:
If the selling price of 20 books is the same as the cost price of 21 books. Find the profit percent.
Solution:
Let cost price of each book be $1
Cost price of 20 books = $1 × 20 = $20.
Selling price of 20 books = cost price of 21 books = $21.
Profit = selling price - cost price
= $21 - $20
= $1
Profits% = profit/cost price × 100
= 1/20 × 100
= 100/20
= 5
Therefore, profit percent is 5%.
Example 3:
Harini sells two watches for $ 1955 each, gaining 15% on one and losing 15% on the other. Find her gain or loss per cent in the whole transaction.
Solution:
SP of the first watch = $ 1955.
Gain% = 15%.
Therefore, CP of the first watch = [{100/(100 + gain %)} × SP]
= $ [{100/(100 + 15)} × 1955]
= $ {(100/115) × 1955}
= $ 1700.
SP of the second watch = $ 1955.
Loss% = 15%.
CP of the second watch = [{100/(100 - loss %)} × SP]
= $ [{100/(100 - 15)} × 1955]
= $ {(100/85) × 1955}
= $ 2300
Total CP of the two watches = $ (1700 + 2300) = $ 4000.
Total SP of the two watches = $ (1955 × 2) = $ 3910.
Since (SP) < (CP), there is a loss in the whole transaction.
Loss = $ (4000 - 3910) = $ 90.
Therefore, Loss% = {(90/4000) × 100} % = 21/4%
Hence, Harini loses 21/4% in the whole transaction.
By selling goods for $9000; a profit of $1000 is made. Find the profit percent.
Solution:
Given, selling price of goods = $9000 and profit made = $1000
Therefore, C.P. = S.P. - profit
= $9000 - $1000
= $8000
And, profit% = (profit/cost price) × 100%
= (1000/8000) × 100%
= (1/8) × 100%
= 12.5%
Therefore, profit percent by selling goods is 12.5%.
Example 2:
If the selling price of 20 books is the same as the cost price of 21 books. Find the profit percent.
Solution:
Let cost price of each book be $1
Cost price of 20 books = $1 × 20 = $20.
Selling price of 20 books = cost price of 21 books = $21.
Profit = selling price - cost price
= $21 - $20
= $1
Profits% = profit/cost price × 100
= 1/20 × 100
= 100/20
= 5
Therefore, profit percent is 5%.
Example 3:
Harini sells two watches for $ 1955 each, gaining 15% on one and losing 15% on the other. Find her gain or loss per cent in the whole transaction.
Solution:
SP of the first watch = $ 1955.
Gain% = 15%.
Therefore, CP of the first watch = [{100/(100 + gain %)} × SP]
= $ [{100/(100 + 15)} × 1955]
= $ {(100/115) × 1955}
= $ 1700.
SP of the second watch = $ 1955.
Loss% = 15%.
CP of the second watch = [{100/(100 - loss %)} × SP]
= $ [{100/(100 - 15)} × 1955]
= $ {(100/85) × 1955}
= $ 2300
Total CP of the two watches = $ (1700 + 2300) = $ 4000.
Total SP of the two watches = $ (1955 × 2) = $ 3910.
Since (SP) < (CP), there is a loss in the whole transaction.
Loss = $ (4000 - 3910) = $ 90.
Therefore, Loss% = {(90/4000) × 100} % = 21/4%
Hence, Harini loses 21/4% in the whole transaction.
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