Question:
Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706
Correct Answer
7110
Solution And Explanation
Solution
Finding the cost price if the sale price and profit percent are known
The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.
Finding the cost price using the formula when the sale price and profit percent are known
Given, the sale price (SP) = $32706
And, the profit = 360%
Then, the Cost Price (CP) = ?
Formula to find the cost price when the sale price and profit percent are known
Cost Price (CP) = 100/100 + gain% × SP
Thus, the Cost Price (CP)
= 100/100 + 360 × 32706
= 100 × 32706/460
= 3270600/460 = 7110
Thus, the Cost Price (CP) = $7110 Answer
Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given
Let the Cost Price (CP) = m
Here given profit = 360%
Calculation of Profit
Profit is calculated on cost price (CP)
Formula to find the Profit = Profit% of CP
Thus, profit on the cost price of m
= 360% of m
= 360% × m
= 360/100 × m
⇒ Profit = 360 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 32706 = m + 360 m/100
⇒ 32706 = 100 m + 360 m/100
⇒ 32706 = 460 m/100
After cross multiplication, we get
32706 × 100 = 460 m
⇒ 460 m = 32706 × 100
⇒ m = 32706 × 100/460
⇒ m = 3270600/460 = 7110
⇒ m = 7110
Thus, the Cost Price (CP) = $7110 Answer
Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given
Given, the sale price (SP) = $32706
And, the profit = 360%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 360% of 100 = 360
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 360
⇒ Sale Price (SP) = 460
∵ If the Sale Price (SP) is 460, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/460
∴ If the Sale Price (SP) is 32706, then the Cost Price (CP)
= 100/460 × 32706
= 100 × 32706/460
= 3270600/460 = 7110
Thus, the Cost Price (CP) = $7110 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $32706
And, the profit = 360%
Then, the Cost Price (CP) = ?
SP = 460% of CP
⇒ SP = 460/100 × CP
⇒ 32706 = 460 CP/100
After cross multiplication
⇒ 32706 × 100 = 460 CP
⇒ 460 CP = 32706 × 100
⇒ CP = 32706 × 100/460
⇒ CP = 3270600/460 = 7110
⇒ CP = $7110 Answer
Similar Questions
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(2) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?
(3) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?
(4) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.
(5) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.
(6) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647
(7) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.
(8) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?
(9) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?
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