Question:
Mr. Oliver loses 81% by selling an article for $742.90. For how much should he sell it to get a profit of 80%?
Correct Answer
7038
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) = $742.9
And, the loss = 81%
Then, the Sale Price (SP) to earn a profit of 80% = ?
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 – 81 × 742.9
= 100/19 × 742.9
= 100 × 742.9/19
= 74290/19 = 3910
Thus, the Cost Price (CP) = $3910
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $3910
And, profit = 80%
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 + 80/100 × 3910
= 180/100 × 3910
= 180 × 3910/100
= 703800/100 = 7038
Thus, Sale Price (SP) at a profit of 80% = $7038 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) = $742.9
And, the loss = 81%
Then, the Sale Price (SP) to earn a profit of 80% = ?
Let the Cost Price (CP) = m
Here given loss = 81%
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
= 81% of m
= 81% × m
= 81/100 × m
⇒ loss = 81 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 742.9 = m – 81 m/100
⇒ 742.9 = 100 m – 81 m/100
⇒ 742.9 = 19 m/100
After cross multiplication, we get
742.9 × 100 = 19 m
⇒ 19 m = 742.9 × 100
⇒ m = 742.9 × 100/19
⇒ m = 74290/19 = 3910
⇒ m = 3910
Thus, the Cost Price (CP) = $3910
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 3910
And, the profit = 80%
Thus, Sale Price (SP)
= Cost Price (CP) + 80% of Cost Price (CP)
= 3910 + 80/100 × 3910
= 3910 + 80 × 3910/100
= 3910 + 312800/100
= 3910 + 3128 = 7038
Thus, Sale Price (SP) at a profit of 80% = $7038 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) = $742.9
And, the loss = 81%
Then, the Sale Price (SP) to earn a profit of 80% = ?
Let, CP = 100
80% profit = 80% of CP
= 80% of 100 = 80
Thus, Sale Price to earn a profit of 80% = CP + 80
= 100 + 80 = 180
⇒ Sale Price to earn a profit of 80% = 180
81% loss = 81% of CP
= 81% of 100 = 81
Thus, Sale Price at a loss of 81% = CP – Loss
= 100 – 81 = 19
⇒ Sale Price at a loss of 81% = 19
∵ If the Sale Price is 19, then to earn a profit of 80% the Sale Price should be = 180
∴ If the Sale Price is 1, then to earn a profit of 80% the Sale Price should be
= 180/19
∴ If the Sale Price is 742.9, then to earn a profit of 80% the Sale Price should be
= 180/19 × 742.9
= 180 × 742.9/19
= 133722/19 = 7038
Thus, Sale Price to get a profit of 80% = $7038 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) = $742.9
And, the loss = 81%
Then, the Sale Price (SP) to earn a profit of 80% = ?
Here, the Sale Price at a loss of 81 = $742.9
This means 19% of the Cost Price (CP) = 742.9
Therefore, 1% of the Cost Price (CP) = 742.9/19
Therefore, 100% of the Cost Price (CP)
= 742.9/19 × 100 = 3910
Thus, the Cost Price (CP) = $3910
Now, we need to find the Sale Price at a profit of 80%
Thus, Sale Price at a profit of 80%
= 180% of the Cost Price (CP)
= 180% of 3910
= 180/100 × 3910 = 7038
Thus, the Cost Price at a profit of 80% = $7038 Answer
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