Question:
Find the cost price, if Mrs. Barbara earns a profit of 275% by selling some items for $20287.50
Correct Answer
5410
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) = $20287.5
And, the profit = 275%
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 + 275 × 20287.5
= 100 × 20287.5/375
= 2028750/375 = 5410
Thus, the Cost Price (CP) = $5410 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 = 275%
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
= 275% of m
= 275% × m
= 275/100 × m
⇒ Profit = 275 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 20287.5 = m + 275 m/100
⇒ 20287.5 = 100 m + 275 m/100
⇒ 20287.5 = 375 m/100
After cross multiplication, we get
20287.5 × 100 = 375 m
⇒ 375 m = 20287.5 × 100
⇒ m = 20287.5 × 100/375
⇒ m = 2028750/375 = 5410
⇒ m = 5410
Thus, the Cost Price (CP) = $5410 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) = $20287.5
And, the profit = 275%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 275% of 100 = 275
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 275
⇒ Sale Price (SP) = 375
∵ If the Sale Price (SP) is 375, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/375
∴ If the Sale Price (SP) is 20287.5, then the Cost Price (CP)
= 100/375 × 20287.5
= 100 × 20287.5/375
= 2028750/375 = 5410
Thus, the Cost Price (CP) = $5410 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $20287.5
And, the profit = 275%
Then, the Cost Price (CP) = ?
SP = 375% of CP
⇒ SP = 375/100 × CP
⇒ 20287.5 = 375 CP/100
After cross multiplication
⇒ 20287.5 × 100 = 375 CP
⇒ 375 CP = 20287.5 × 100
⇒ CP = 20287.5 × 100/375
⇒ CP = 2028750/375 = 5410
⇒ CP = $5410 Answer
Similar Questions
(1) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?
(2) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?
(3) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?
(4) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?
(5) Mr. James loses 24% after selling an article for $805.60. For how much should he sell it to get a profit of 23%?
(6) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647
(7) A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?
(8) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?
(9) Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640
(10) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.