Question:
John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?
Correct Answer
310
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) = $372
And, the profit = 20%
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 + 20 × 372
= 100 × 372/120
= 37200/120 = 310
Thus, the Cost Price (CP) = $310 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 = 20%
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
= 20% of m
= 20% × m
= 20/100 × m
⇒ Profit = 20 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 372 = m + 20 m/100
⇒ 372 = 100 m + 20 m/100
⇒ 372 = 120 m/100
After cross multiplication, we get
372 × 100 = 120 m
⇒ 120 m = 372 × 100
⇒ m = 372 × 100/120
⇒ m = 37200/120 = 310
⇒ m = 310
Thus, the Cost Price (CP) = $310 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) = $372
And, the profit = 20%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 20% of 100 = 20
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 20
⇒ Sale Price (SP) = 120
∵ If the Sale Price (SP) is 120, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/120
∴ If the Sale Price (SP) is 372, then the Cost Price (CP)
= 100/120 × 372
= 100 × 372/120
= 37200/120 = 310
Thus, the Cost Price (CP) = $310 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $372
And, the profit = 20%
Then, the Cost Price (CP) = ?
SP = 120% of CP
⇒ SP = 120/100 × CP
⇒ 372 = 120 CP/100
After cross multiplication
⇒ 372 × 100 = 120 CP
⇒ 120 CP = 372 × 100
⇒ CP = 372 × 100/120
⇒ CP = 37200/120 = 310
⇒ CP = $310 Answer
Similar Questions
(1) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?
(2) A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent.
(3) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?
(4) What will be the earnings in percent if a vendor buys 45 articles for $1 and sells 44 articles for $1?
(5) What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50
(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) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?
(9) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.
(10) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.