Question:
For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.
Correct Answer
510.6
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) = $404.8
And, the loss = 12%
Then, the Sale Price (SP) to earn a profit of 11% = ?
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 – 12 × 404.8
= 100/88 × 404.8
= 100 × 404.8/88
= 40480/88 = 460
Thus, the Cost Price (CP) = $460
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $460
And, profit = 11%
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 + 11/100 × 460
= 111/100 × 460
= 111 × 460/100
= 51060/100 = 510.6
Thus, Sale Price (SP) at a profit of 11% = $510.6 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) = $404.8
And, the loss = 12%
Then, the Sale Price (SP) to earn a profit of 11% = ?
Let the Cost Price (CP) = m
Here given loss = 12%
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
= 12% of m
= 12% × m
= 12/100 × m
⇒ loss = 12 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 404.8 = m – 12 m/100
⇒ 404.8 = 100 m – 12 m/100
⇒ 404.8 = 88 m/100
After cross multiplication, we get
404.8 × 100 = 88 m
⇒ 88 m = 404.8 × 100
⇒ m = 404.8 × 100/88
⇒ m = 40480/88 = 460
⇒ m = 460
Thus, the Cost Price (CP) = $460
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 460
And, the profit = 11%
Thus, Sale Price (SP)
= Cost Price (CP) + 11% of Cost Price (CP)
= 460 + 11/100 × 460
= 460 + 11 × 460/100
= 460 + 5060/100
= 460 + 50.6 = 510.6
Thus, Sale Price (SP) at a profit of 11% = $510.6 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) = $404.8
And, the loss = 12%
Then, the Sale Price (SP) to earn a profit of 11% = ?
Let, CP = 100
11% profit = 11% of CP
= 11% of 100 = 11
Thus, Sale Price to earn a profit of 11% = CP + 11
= 100 + 11 = 111
⇒ Sale Price to earn a profit of 11% = 111
12% loss = 12% of CP
= 12% of 100 = 12
Thus, Sale Price at a loss of 12% = CP – Loss
= 100 – 12 = 88
⇒ Sale Price at a loss of 12% = 88
∵ If the Sale Price is 88, then to earn a profit of 11% the Sale Price should be = 111
∴ If the Sale Price is 1, then to earn a profit of 11% the Sale Price should be
= 111/88
∴ If the Sale Price is 404.8, then to earn a profit of 11% the Sale Price should be
= 111/88 × 404.8
= 111 × 404.8/88
= 44932.8/88 = 510.6
Thus, Sale Price to get a profit of 11% = $510.6 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) = $404.8
And, the loss = 12%
Then, the Sale Price (SP) to earn a profit of 11% = ?
Here, the Sale Price at a loss of 12 = $404.8
This means 88% of the Cost Price (CP) = 404.8
Therefore, 1% of the Cost Price (CP) = 404.8/88
Therefore, 100% of the Cost Price (CP)
= 404.8/88 × 100 = 460
Thus, the Cost Price (CP) = $460
Now, we need to find the Sale Price at a profit of 11%
Thus, Sale Price at a profit of 11%
= 111% of the Cost Price (CP)
= 111% of 460
= 111/100 × 460 = 510.6
Thus, the Cost Price at a profit of 11% = $510.6 Answer
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