Question:
A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?
Correct Answer
1161.6
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) = $748.8
And, the loss = 22%
Then, the Sale Price (SP) to earn a profit of 21% = ?
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 – 22 × 748.8
= 100/78 × 748.8
= 100 × 748.8/78
= 74880/78 = 960
Thus, the Cost Price (CP) = $960
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $960
And, profit = 21%
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 + 21/100 × 960
= 121/100 × 960
= 121 × 960/100
= 116160/100 = 1161.6
Thus, Sale Price (SP) at a profit of 21% = $1161.6 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) = $748.8
And, the loss = 22%
Then, the Sale Price (SP) to earn a profit of 21% = ?
Let the Cost Price (CP) = m
Here given loss = 22%
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
= 22% of m
= 22% × m
= 22/100 × m
⇒ loss = 22 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 748.8 = m – 22 m/100
⇒ 748.8 = 100 m – 22 m/100
⇒ 748.8 = 78 m/100
After cross multiplication, we get
748.8 × 100 = 78 m
⇒ 78 m = 748.8 × 100
⇒ m = 748.8 × 100/78
⇒ m = 74880/78 = 960
⇒ m = 960
Thus, the Cost Price (CP) = $960
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 960
And, the profit = 21%
Thus, Sale Price (SP)
= Cost Price (CP) + 21% of Cost Price (CP)
= 960 + 21/100 × 960
= 960 + 21 × 960/100
= 960 + 20160/100
= 960 + 201.6 = 1161.6
Thus, Sale Price (SP) at a profit of 21% = $1161.6 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) = $748.8
And, the loss = 22%
Then, the Sale Price (SP) to earn a profit of 21% = ?
Let, CP = 100
21% profit = 21% of CP
= 21% of 100 = 21
Thus, Sale Price to earn a profit of 21% = CP + 21
= 100 + 21 = 121
⇒ Sale Price to earn a profit of 21% = 121
22% loss = 22% of CP
= 22% of 100 = 22
Thus, Sale Price at a loss of 22% = CP – Loss
= 100 – 22 = 78
⇒ Sale Price at a loss of 22% = 78
∵ If the Sale Price is 78, then to earn a profit of 21% the Sale Price should be = 121
∴ If the Sale Price is 1, then to earn a profit of 21% the Sale Price should be
= 121/78
∴ If the Sale Price is 748.8, then to earn a profit of 21% the Sale Price should be
= 121/78 × 748.8
= 121 × 748.8/78
= 90604.8/78 = 1161.6
Thus, Sale Price to get a profit of 21% = $1161.6 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) = $748.8
And, the loss = 22%
Then, the Sale Price (SP) to earn a profit of 21% = ?
Here, the Sale Price at a loss of 22 = $748.8
This means 78% of the Cost Price (CP) = 748.8
Therefore, 1% of the Cost Price (CP) = 748.8/78
Therefore, 100% of the Cost Price (CP)
= 748.8/78 × 100 = 960
Thus, the Cost Price (CP) = $960
Now, we need to find the Sale Price at a profit of 21%
Thus, Sale Price at a profit of 21%
= 121% of the Cost Price (CP)
= 121% of 960
= 121/100 × 960 = 1161.6
Thus, the Cost Price at a profit of 21% = $1161.6 Answer
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(2) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.
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(4) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.
(5) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.
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(7) Mr. Donald loses 88% by selling an article for $511.20. For how much should he sell it to get a profit of 87%?
(8) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?
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