Question:
A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?
Correct Answer
4547.4
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) = $1144
And, the loss = 60%
Then, the Sale Price (SP) to earn a profit of 59% = ?
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 – 60 × 1144
= 100/40 × 1144
= 100 × 1144/40
= 114400/40 = 2860
Thus, the Cost Price (CP) = $2860
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $2860
And, profit = 59%
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 + 59/100 × 2860
= 159/100 × 2860
= 159 × 2860/100
= 454740/100 = 4547.4
Thus, Sale Price (SP) at a profit of 59% = $4547.4 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) = $1144
And, the loss = 60%
Then, the Sale Price (SP) to earn a profit of 59% = ?
Let the Cost Price (CP) = m
Here given loss = 60%
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
= 60% of m
= 60% × m
= 60/100 × m
⇒ loss = 60 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1144 = m – 60 m/100
⇒ 1144 = 100 m – 60 m/100
⇒ 1144 = 40 m/100
After cross multiplication, we get
1144 × 100 = 40 m
⇒ 40 m = 1144 × 100
⇒ m = 1144 × 100/40
⇒ m = 114400/40 = 2860
⇒ m = 2860
Thus, the Cost Price (CP) = $2860
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 2860
And, the profit = 59%
Thus, Sale Price (SP)
= Cost Price (CP) + 59% of Cost Price (CP)
= 2860 + 59/100 × 2860
= 2860 + 59 × 2860/100
= 2860 + 168740/100
= 2860 + 1687.4 = 4547.4
Thus, Sale Price (SP) at a profit of 59% = $4547.4 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) = $1144
And, the loss = 60%
Then, the Sale Price (SP) to earn a profit of 59% = ?
Let, CP = 100
59% profit = 59% of CP
= 59% of 100 = 59
Thus, Sale Price to earn a profit of 59% = CP + 59
= 100 + 59 = 159
⇒ Sale Price to earn a profit of 59% = 159
60% loss = 60% of CP
= 60% of 100 = 60
Thus, Sale Price at a loss of 60% = CP – Loss
= 100 – 60 = 40
⇒ Sale Price at a loss of 60% = 40
∵ If the Sale Price is 40, then to earn a profit of 59% the Sale Price should be = 159
∴ If the Sale Price is 1, then to earn a profit of 59% the Sale Price should be
= 159/40
∴ If the Sale Price is 1144, then to earn a profit of 59% the Sale Price should be
= 159/40 × 1144
= 159 × 1144/40
= 181896/40 = 4547.4
Thus, Sale Price to get a profit of 59% = $4547.4 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) = $1144
And, the loss = 60%
Then, the Sale Price (SP) to earn a profit of 59% = ?
Here, the Sale Price at a loss of 60 = $1144
This means 40% of the Cost Price (CP) = 1144
Therefore, 1% of the Cost Price (CP) = 1144/40
Therefore, 100% of the Cost Price (CP)
= 1144/40 × 100 = 2860
Thus, the Cost Price (CP) = $2860
Now, we need to find the Sale Price at a profit of 59%
Thus, Sale Price at a profit of 59%
= 159% of the Cost Price (CP)
= 159% of 2860
= 159/100 × 2860 = 4547.4
Thus, the Cost Price at a profit of 59% = $4547.4 Answer
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(3) Mr. Donald loses 86% by selling an article for $582.40. For how much should he sell it to get a profit of 85%?
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(7) If a dealer gets a loss of 75% by selling 200 boxes of apple for $3702.50 then find the cost price.
(8) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50
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