Question:
If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?
Correct Answer
6610
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) = $28753.5
And, the profit = 335%
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 + 335 × 28753.5
= 100 × 28753.5/435
= 2875350/435 = 6610
Thus, the Cost Price (CP) = $6610 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 = 335%
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
= 335% of m
= 335% × m
= 335/100 × m
⇒ Profit = 335 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 28753.5 = m + 335 m/100
⇒ 28753.5 = 100 m + 335 m/100
⇒ 28753.5 = 435 m/100
After cross multiplication, we get
28753.5 × 100 = 435 m
⇒ 435 m = 28753.5 × 100
⇒ m = 28753.5 × 100/435
⇒ m = 2875350/435 = 6610
⇒ m = 6610
Thus, the Cost Price (CP) = $6610 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) = $28753.5
And, the profit = 335%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 335% of 100 = 335
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 335
⇒ Sale Price (SP) = 435
∵ If the Sale Price (SP) is 435, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/435
∴ If the Sale Price (SP) is 28753.5, then the Cost Price (CP)
= 100/435 × 28753.5
= 100 × 28753.5/435
= 2875350/435 = 6610
Thus, the Cost Price (CP) = $6610 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $28753.5
And, the profit = 335%
Then, the Cost Price (CP) = ?
SP = 435% of CP
⇒ SP = 435/100 × CP
⇒ 28753.5 = 435 CP/100
After cross multiplication
⇒ 28753.5 × 100 = 435 CP
⇒ 435 CP = 28753.5 × 100
⇒ CP = 28753.5 × 100/435
⇒ CP = 2875350/435 = 6610
⇒ CP = $6610 Answer
Similar Questions
(1) Find the cost price, if a trader gets a loss of 68% by selling five bags of rice for $4291.20
(2) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?
(3) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?
(4) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?
(5) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.
(6) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?
(7) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.
(8) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?
(9) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.
(10) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20