Question:
Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?
Correct Answer
8379
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) = $396.9
And, the loss = 91%
Then, the Sale Price (SP) to earn a profit of 90% = ?
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 – 91 × 396.9
= 100/9 × 396.9
= 100 × 396.9/9
= 39690/9 = 4410
Thus, the Cost Price (CP) = $4410
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $4410
And, profit = 90%
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 + 90/100 × 4410
= 190/100 × 4410
= 190 × 4410/100
= 837900/100 = 8379
Thus, Sale Price (SP) at a profit of 90% = $8379 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) = $396.9
And, the loss = 91%
Then, the Sale Price (SP) to earn a profit of 90% = ?
Let the Cost Price (CP) = m
Here given loss = 91%
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
= 91% of m
= 91% × m
= 91/100 × m
⇒ loss = 91 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 396.9 = m – 91 m/100
⇒ 396.9 = 100 m – 91 m/100
⇒ 396.9 = 9 m/100
After cross multiplication, we get
396.9 × 100 = 9 m
⇒ 9 m = 396.9 × 100
⇒ m = 396.9 × 100/9
⇒ m = 39690/9 = 4410
⇒ m = 4410
Thus, the Cost Price (CP) = $4410
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 4410
And, the profit = 90%
Thus, Sale Price (SP)
= Cost Price (CP) + 90% of Cost Price (CP)
= 4410 + 90/100 × 4410
= 4410 + 90 × 4410/100
= 4410 + 396900/100
= 4410 + 3969 = 8379
Thus, Sale Price (SP) at a profit of 90% = $8379 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) = $396.9
And, the loss = 91%
Then, the Sale Price (SP) to earn a profit of 90% = ?
Let, CP = 100
90% profit = 90% of CP
= 90% of 100 = 90
Thus, Sale Price to earn a profit of 90% = CP + 90
= 100 + 90 = 190
⇒ Sale Price to earn a profit of 90% = 190
91% loss = 91% of CP
= 91% of 100 = 91
Thus, Sale Price at a loss of 91% = CP – Loss
= 100 – 91 = 9
⇒ Sale Price at a loss of 91% = 9
∵ If the Sale Price is 9, then to earn a profit of 90% the Sale Price should be = 190
∴ If the Sale Price is 1, then to earn a profit of 90% the Sale Price should be
= 190/9
∴ If the Sale Price is 396.9, then to earn a profit of 90% the Sale Price should be
= 190/9 × 396.9
= 190 × 396.9/9
= 75411/9 = 8379
Thus, Sale Price to get a profit of 90% = $8379 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) = $396.9
And, the loss = 91%
Then, the Sale Price (SP) to earn a profit of 90% = ?
Here, the Sale Price at a loss of 91 = $396.9
This means 9% of the Cost Price (CP) = 396.9
Therefore, 1% of the Cost Price (CP) = 396.9/9
Therefore, 100% of the Cost Price (CP)
= 396.9/9 × 100 = 4410
Thus, the Cost Price (CP) = $4410
Now, we need to find the Sale Price at a profit of 90%
Thus, Sale Price at a profit of 90%
= 190% of the Cost Price (CP)
= 190% of 4410
= 190/100 × 4410 = 8379
Thus, the Cost Price at a profit of 90% = $8379 Answer
Similar Questions
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(2) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?
(3) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.
(4) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.
(5) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.
(6) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.
(7) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.
(8) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?
(9) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?
(10) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?