Question:
By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.
Correct Answer
1710
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) = $3249
And, the profit = 90%
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 + 90 × 3249
= 100 × 3249/190
= 324900/190 = 1710
Thus, the Cost Price (CP) = $1710 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 = 90%
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
= 90% of m
= 90% × m
= 90/100 × m
⇒ Profit = 90 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 3249 = m + 90 m/100
⇒ 3249 = 100 m + 90 m/100
⇒ 3249 = 190 m/100
After cross multiplication, we get
3249 × 100 = 190 m
⇒ 190 m = 3249 × 100
⇒ m = 3249 × 100/190
⇒ m = 324900/190 = 1710
⇒ m = 1710
Thus, the Cost Price (CP) = $1710 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) = $3249
And, the profit = 90%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 90% of 100 = 90
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 90
⇒ Sale Price (SP) = 190
∵ If the Sale Price (SP) is 190, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/190
∴ If the Sale Price (SP) is 3249, then the Cost Price (CP)
= 100/190 × 3249
= 100 × 3249/190
= 324900/190 = 1710
Thus, the Cost Price (CP) = $1710 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $3249
And, the profit = 90%
Then, the Cost Price (CP) = ?
SP = 190% of CP
⇒ SP = 190/100 × CP
⇒ 3249 = 190 CP/100
After cross multiplication
⇒ 3249 × 100 = 190 CP
⇒ 190 CP = 3249 × 100
⇒ CP = 3249 × 100/190
⇒ CP = 324900/190 = 1710
⇒ CP = $1710 Answer
Similar Questions
(1) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.
(2) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?
(3) Mr. Steven loses 92% by selling an article for $356.80. For how much should he sell it to get a profit of 91%?
(4) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.
(5) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and 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) Find the earnings percentage if a vendor buys 49 articles for $1 and sells 48 articles for $1.
(8) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.
(9) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?
(10) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?