Question:
Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5
Correct Answer
5210
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) = $19016.5
And, the profit = 265%
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 + 265 × 19016.5
= 100 × 19016.5/365
= 1901650/365 = 5210
Thus, the Cost Price (CP) = $5210 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 = 265%
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
= 265% of m
= 265% × m
= 265/100 × m
⇒ Profit = 265 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 19016.5 = m + 265 m/100
⇒ 19016.5 = 100 m + 265 m/100
⇒ 19016.5 = 365 m/100
After cross multiplication, we get
19016.5 × 100 = 365 m
⇒ 365 m = 19016.5 × 100
⇒ m = 19016.5 × 100/365
⇒ m = 1901650/365 = 5210
⇒ m = 5210
Thus, the Cost Price (CP) = $5210 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) = $19016.5
And, the profit = 265%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 265% of 100 = 265
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 265
⇒ Sale Price (SP) = 365
∵ If the Sale Price (SP) is 365, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/365
∴ If the Sale Price (SP) is 19016.5, then the Cost Price (CP)
= 100/365 × 19016.5
= 100 × 19016.5/365
= 1901650/365 = 5210
Thus, the Cost Price (CP) = $5210 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $19016.5
And, the profit = 265%
Then, the Cost Price (CP) = ?
SP = 365% of CP
⇒ SP = 365/100 × CP
⇒ 19016.5 = 365 CP/100
After cross multiplication
⇒ 19016.5 × 100 = 365 CP
⇒ 365 CP = 19016.5 × 100
⇒ CP = 19016.5 × 100/365
⇒ CP = 1901650/365 = 5210
⇒ CP = $5210 Answer
Similar Questions
(1) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.
(2) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?
(3) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?
(4) If Boby buys 69 pencils for $1 and sells them at a rate of 68 per $1 then, find the earnings in percentage.
(5) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048
(6) Find the cost price, if a trader earns a profit of 395% by selling an article for $38659.5
(7) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?
(8) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?
(9) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?
(10) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.