Question:
By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.
Correct Answer
5510
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) = $20938
And, the profit = 280%
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 + 280 × 20938
= 100 × 20938/380
= 2093800/380 = 5510
Thus, the Cost Price (CP) = $5510 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 = 280%
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
= 280% of m
= 280% × m
= 280/100 × m
⇒ Profit = 280 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 20938 = m + 280 m/100
⇒ 20938 = 100 m + 280 m/100
⇒ 20938 = 380 m/100
After cross multiplication, we get
20938 × 100 = 380 m
⇒ 380 m = 20938 × 100
⇒ m = 20938 × 100/380
⇒ m = 2093800/380 = 5510
⇒ m = 5510
Thus, the Cost Price (CP) = $5510 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) = $20938
And, the profit = 280%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 280% of 100 = 280
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 280
⇒ Sale Price (SP) = 380
∵ If the Sale Price (SP) is 380, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/380
∴ If the Sale Price (SP) is 20938, then the Cost Price (CP)
= 100/380 × 20938
= 100 × 20938/380
= 2093800/380 = 5510
Thus, the Cost Price (CP) = $5510 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $20938
And, the profit = 280%
Then, the Cost Price (CP) = ?
SP = 380% of CP
⇒ SP = 380/100 × CP
⇒ 20938 = 380 CP/100
After cross multiplication
⇒ 20938 × 100 = 380 CP
⇒ 380 CP = 20938 × 100
⇒ CP = 20938 × 100/380
⇒ CP = 2093800/380 = 5510
⇒ CP = $5510 Answer
Similar Questions
(1) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?
(2) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30
(3) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?
(4) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.
(5) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70
(6) Find the cost price, if a trader earns a profit of 395% by selling an article for $38659.5
(7) If a trader earns a profit of 10% by selling rice for $121 per kg, then find the cost price of the rice
(8) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.
(9) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.
(10) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.