Question:
By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.
Correct Answer
4110
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) = $12741
And, the profit = 210%
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 + 210 × 12741
= 100 × 12741/310
= 1274100/310 = 4110
Thus, the Cost Price (CP) = $4110 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 = 210%
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
= 210% of m
= 210% × m
= 210/100 × m
⇒ Profit = 210 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 12741 = m + 210 m/100
⇒ 12741 = 100 m + 210 m/100
⇒ 12741 = 310 m/100
After cross multiplication, we get
12741 × 100 = 310 m
⇒ 310 m = 12741 × 100
⇒ m = 12741 × 100/310
⇒ m = 1274100/310 = 4110
⇒ m = 4110
Thus, the Cost Price (CP) = $4110 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) = $12741
And, the profit = 210%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 210% of 100 = 210
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 210
⇒ Sale Price (SP) = 310
∵ If the Sale Price (SP) is 310, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/310
∴ If the Sale Price (SP) is 12741, then the Cost Price (CP)
= 100/310 × 12741
= 100 × 12741/310
= 1274100/310 = 4110
Thus, the Cost Price (CP) = $4110 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $12741
And, the profit = 210%
Then, the Cost Price (CP) = ?
SP = 310% of CP
⇒ SP = 310/100 × CP
⇒ 12741 = 310 CP/100
After cross multiplication
⇒ 12741 × 100 = 310 CP
⇒ 310 CP = 12741 × 100
⇒ CP = 12741 × 100/310
⇒ CP = 1274100/310 = 4110
⇒ CP = $4110 Answer
Similar Questions
(1) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.
(2) Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%
(3) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?
(4) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?
(5) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?
(6) A shopkeeper loses 51% by selling an article for $1180.90. For how much should he sell it to get a profit of 50%?
(7) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.
(8) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?
(9) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.
(10) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.