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) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?
(2) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?
(3) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?
(4) Find the earnings percentage if a vendor buys 49 articles for $1 and sells 48 articles for $1.
(5) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?
(6) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.
(7) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.
(8) Find the cost price, if a house broker earns a profit of 365% by selling a plot for $33526.5
(9) A trader loses 55% by selling an article for $1174.50. For how much should he sell it to get a profit of 54%?
(10) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.