Question:
Mr. Steven loses 94% by selling an article for $273.60. For how much should he sell it to get a profit of 93%?
Correct Answer
8800.8
Solution And Explanation
Strategy to solve the question
Step (1) Calculate the cost price at given loss percent and the sale price.
Step (2) After gettting the cost price find the sale price at given profit percent.
Solution
Method (1) Formula Method
Finding the Sale Price to earn a profit using formula when the Sale Price at a loss is given
Given, the sale price (SP) = $273.6
And, the loss = 94%
Then, the Sale Price (SP) to earn a profit of 93% = ?
Formula to find the cost price when the sale price and loss percent are known
Cost Price (CP) = 100/100 – gain% × SP
Thus, the Cost Price (CP)
= 100/100 – 94 × 273.6
= 100/6 × 273.6
= 100 × 273.6/6
= 27360/6 = 4560
Thus, the Cost Price (CP) = $4560
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $4560
And, profit = 93%
Thus Sale Price (SP) = ?
Formula to find the Sale Price (SP) when the cost price (CP) and profit percent are known
Sale Price (SP) = 100 + gain%/100 × Cost Price (CP)
Thus, the Sale Price (SP)
= 100 + 93/100 × 4560
= 193/100 × 4560
= 193 × 4560/100
= 880080/100 = 8800.8
Thus, Sale Price (SP) at a profit of 93% = $8800.8 Answer
Method (2) Algebraic Method
Finding the Sale Price (SP) to earn the given profit using the Algebraic Method when the Sale Pric (SP) at a loss percent is given
Given, the sale price (SP) = $273.6
And, the loss = 94%
Then, the Sale Price (SP) to earn a profit of 93% = ?
Let the Cost Price (CP) = m
Here given loss = 94%
Calculation of loss
loss is calculated on cost price (CP)
Formula to find the loss = loss% of CP
Thus, loss on the cost price of m
= 94% of m
= 94% × m
= 94/100 × m
⇒ loss = 94 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 273.6 = m – 94 m/100
⇒ 273.6 = 100 m – 94 m/100
⇒ 273.6 = 6 m/100
After cross multiplication, we get
273.6 × 100 = 6 m
⇒ 6 m = 273.6 × 100
⇒ m = 273.6 × 100/6
⇒ m = 27360/6 = 4560
⇒ m = 4560
Thus, the Cost Price (CP) = $4560
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 4560
And, the profit = 93%
Thus, Sale Price (SP)
= Cost Price (CP) + 93% of Cost Price (CP)
= 4560 + 93/100 × 4560
= 4560 + 93 × 4560/100
= 4560 + 424080/100
= 4560 + 4240.8 = 8800.8
Thus, Sale Price (SP) at a profit of 93% = $8800.8 Answer
Method (3) Unitary Method
Finding the Sale Price (SP) to earn a given profit when the Sale price (SP) at a loss is given
Given, the sale price (SP) = $273.6
And, the loss = 94%
Then, the Sale Price (SP) to earn a profit of 93% = ?
Let, CP = 100
93% profit = 93% of CP
= 93% of 100 = 93
Thus, Sale Price to earn a profit of 93% = CP + 93
= 100 + 93 = 193
⇒ Sale Price to earn a profit of 93% = 193
94% loss = 94% of CP
= 94% of 100 = 94
Thus, Sale Price at a loss of 94% = CP – Loss
= 100 – 94 = 6
⇒ Sale Price at a loss of 94% = 6
∵ If the Sale Price is 6, then to earn a profit of 93% the Sale Price should be = 193
∴ If the Sale Price is 1, then to earn a profit of 93% the Sale Price should be
= 193/6
∴ If the Sale Price is 273.6, then to earn a profit of 93% the Sale Price should be
= 193/6 × 273.6
= 193 × 273.6/6
= 52804.8/6 = 8800.8
Thus, Sale Price to get a profit of 93% = $8800.8 Answer
Method (4) Shortcut Method
Shortcut Method to find the Sale Price at a given profit when Sale Price at a loss is given
Given, the sale price (SP) = $273.6
And, the loss = 94%
Then, the Sale Price (SP) to earn a profit of 93% = ?
Here, the Sale Price at a loss of 94 = $273.6
This means 6% of the Cost Price (CP) = 273.6
Therefore, 1% of the Cost Price (CP) = 273.6/6
Therefore, 100% of the Cost Price (CP)
= 273.6/6 × 100 = 4560
Thus, the Cost Price (CP) = $4560
Now, we need to find the Sale Price at a profit of 93%
Thus, Sale Price at a profit of 93%
= 193% of the Cost Price (CP)
= 193% of 4560
= 193/100 × 4560 = 8800.8
Thus, the Cost Price at a profit of 93% = $8800.8 Answer
Similar Questions
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(2) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?
(3) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?
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