Question:
William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?
Correct Answer
2854.2
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) = $1145.7
And, the loss = 43%
Then, the Sale Price (SP) to earn a profit of 42% = ?
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 – 43 × 1145.7
= 100/57 × 1145.7
= 100 × 1145.7/57
= 114570/57 = 2010
Thus, the Cost Price (CP) = $2010
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $2010
And, profit = 42%
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 + 42/100 × 2010
= 142/100 × 2010
= 142 × 2010/100
= 285420/100 = 2854.2
Thus, Sale Price (SP) at a profit of 42% = $2854.2 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) = $1145.7
And, the loss = 43%
Then, the Sale Price (SP) to earn a profit of 42% = ?
Let the Cost Price (CP) = m
Here given loss = 43%
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
= 43% of m
= 43% × m
= 43/100 × m
⇒ loss = 43 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1145.7 = m – 43 m/100
⇒ 1145.7 = 100 m – 43 m/100
⇒ 1145.7 = 57 m/100
After cross multiplication, we get
1145.7 × 100 = 57 m
⇒ 57 m = 1145.7 × 100
⇒ m = 1145.7 × 100/57
⇒ m = 114570/57 = 2010
⇒ m = 2010
Thus, the Cost Price (CP) = $2010
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 2010
And, the profit = 42%
Thus, Sale Price (SP)
= Cost Price (CP) + 42% of Cost Price (CP)
= 2010 + 42/100 × 2010
= 2010 + 42 × 2010/100
= 2010 + 84420/100
= 2010 + 844.2 = 2854.2
Thus, Sale Price (SP) at a profit of 42% = $2854.2 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) = $1145.7
And, the loss = 43%
Then, the Sale Price (SP) to earn a profit of 42% = ?
Let, CP = 100
42% profit = 42% of CP
= 42% of 100 = 42
Thus, Sale Price to earn a profit of 42% = CP + 42
= 100 + 42 = 142
⇒ Sale Price to earn a profit of 42% = 142
43% loss = 43% of CP
= 43% of 100 = 43
Thus, Sale Price at a loss of 43% = CP – Loss
= 100 – 43 = 57
⇒ Sale Price at a loss of 43% = 57
∵ If the Sale Price is 57, then to earn a profit of 42% the Sale Price should be = 142
∴ If the Sale Price is 1, then to earn a profit of 42% the Sale Price should be
= 142/57
∴ If the Sale Price is 1145.7, then to earn a profit of 42% the Sale Price should be
= 142/57 × 1145.7
= 142 × 1145.7/57
= 162689.4/57 = 2854.2
Thus, Sale Price to get a profit of 42% = $2854.2 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) = $1145.7
And, the loss = 43%
Then, the Sale Price (SP) to earn a profit of 42% = ?
Here, the Sale Price at a loss of 43 = $1145.7
This means 57% of the Cost Price (CP) = 1145.7
Therefore, 1% of the Cost Price (CP) = 1145.7/57
Therefore, 100% of the Cost Price (CP)
= 1145.7/57 × 100 = 2010
Thus, the Cost Price (CP) = $2010
Now, we need to find the Sale Price at a profit of 42%
Thus, Sale Price at a profit of 42%
= 142% of the Cost Price (CP)
= 142% of 2010
= 142/100 × 2010 = 2854.2
Thus, the Cost Price at a profit of 42% = $2854.2 Answer
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