Question:
Peter loses 3% by selling an article for $9.70. For how much should he sell it to get a profit of 2%?
Correct Answer
10.2
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) = $9.7
And, the loss = 3%
Then, the Sale Price (SP) to earn a profit of 2% = ?
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 – 3 × 9.7
= 100/97 × 9.7
= 100 × 9.7/97
= 970/97 = 10
Thus, the Cost Price (CP) = $10
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $10
And, profit = 2%
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 + 2/100 × 10
= 102/100 × 10
= 102 × 10/100
= 1020/100 = 10.2
Thus, Sale Price (SP) at a profit of 2% = $10.2 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) = $9.7
And, the loss = 3%
Then, the Sale Price (SP) to earn a profit of 2% = ?
Let the Cost Price (CP) = m
Here given loss = 3%
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
= 3% of m
= 3% × m
= 3/100 × m
⇒ loss = 3 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 9.7 = m – 3 m/100
⇒ 9.7 = 100 m – 3 m/100
⇒ 9.7 = 97 m/100
After cross multiplication, we get
9.7 × 100 = 97 m
⇒ 97 m = 9.7 × 100
⇒ m = 9.7 × 100/97
⇒ m = 970/97 = 10
⇒ m = 10
Thus, the Cost Price (CP) = $10
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 10
And, the profit = 2%
Thus, Sale Price (SP)
= Cost Price (CP) + 2% of Cost Price (CP)
= 10 + 2/100 × 10
= 10 + 2 × 10/100
= 10 + 20/100
= 10 + 0.2 = 10.2
Thus, Sale Price (SP) at a profit of 2% = $10.2 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) = $9.7
And, the loss = 3%
Then, the Sale Price (SP) to earn a profit of 2% = ?
Let, CP = 100
2% profit = 2% of CP
= 2% of 100 = 2
Thus, Sale Price to earn a profit of 2% = CP + 2
= 100 + 2 = 102
⇒ Sale Price to earn a profit of 2% = 102
3% loss = 3% of CP
= 3% of 100 = 3
Thus, Sale Price at a loss of 3% = CP – Loss
= 100 – 3 = 97
⇒ Sale Price at a loss of 3% = 97
∵ If the Sale Price is 97, then to earn a profit of 2% the Sale Price should be = 102
∴ If the Sale Price is 1, then to earn a profit of 2% the Sale Price should be
= 102/97
∴ If the Sale Price is 9.7, then to earn a profit of 2% the Sale Price should be
= 102/97 × 9.7
= 102 × 9.7/97
= 989.4/97 = 10.2
Thus, Sale Price to get a profit of 2% = $10.2 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) = $9.7
And, the loss = 3%
Then, the Sale Price (SP) to earn a profit of 2% = ?
Here, the Sale Price at a loss of 3 = $9.7
This means 97% of the Cost Price (CP) = 9.7
Therefore, 1% of the Cost Price (CP) = 9.7/97
Therefore, 100% of the Cost Price (CP)
= 9.7/97 × 100 = 10
Thus, the Cost Price (CP) = $10
Now, we need to find the Sale Price at a profit of 2%
Thus, Sale Price at a profit of 2%
= 102% of the Cost Price (CP)
= 102% of 10
= 102/100 × 10 = 10.2
Thus, the Cost Price at a profit of 2% = $10.2 Answer
Similar Questions
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(2) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?
(3) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?
(4) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?
(5) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.
(6) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718
(7) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?
(8) Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.
(9) Mr. Oliver loses 82% by selling an article for $712.80. For how much should he sell it to get a profit of 81%?
(10) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?