Question:
While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?
Correct Answer
610
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) = $823.5
And, the profit = 35%
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 + 35 × 823.5
= 100 × 823.5/135
= 82350/135 = 610
Thus, the Cost Price (CP) = $610 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 = 35%
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
= 35% of m
= 35% × m
= 35/100 × m
⇒ Profit = 35 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 823.5 = m + 35 m/100
⇒ 823.5 = 100 m + 35 m/100
⇒ 823.5 = 135 m/100
After cross multiplication, we get
823.5 × 100 = 135 m
⇒ 135 m = 823.5 × 100
⇒ m = 823.5 × 100/135
⇒ m = 82350/135 = 610
⇒ m = 610
Thus, the Cost Price (CP) = $610 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) = $823.5
And, the profit = 35%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 35% of 100 = 35
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 35
⇒ Sale Price (SP) = 135
∵ If the Sale Price (SP) is 135, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/135
∴ If the Sale Price (SP) is 823.5, then the Cost Price (CP)
= 100/135 × 823.5
= 100 × 823.5/135
= 82350/135 = 610
Thus, the Cost Price (CP) = $610 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $823.5
And, the profit = 35%
Then, the Cost Price (CP) = ?
SP = 135% of CP
⇒ SP = 135/100 × CP
⇒ 823.5 = 135 CP/100
After cross multiplication
⇒ 823.5 × 100 = 135 CP
⇒ 135 CP = 823.5 × 100
⇒ CP = 823.5 × 100/135
⇒ CP = 82350/135 = 610
⇒ CP = $610 Answer
Similar Questions
(1) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?
(2) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?
(3) Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.
(4) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.
(5) Find the cost price, if a trader gets a loss of 12% by selling some of his stock of fruits for $1944.80. Find the cost price of those stock.
(6) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?
(7) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?
(8) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20
(9) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?
(10) Find the cost price if a broker earned 375% while dealing a house for $35197.50