Question:
Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%
Correct Answer
4310
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) = $13792
And, the profit = 220%
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 + 220 × 13792
= 100 × 13792/320
= 1379200/320 = 4310
Thus, the Cost Price (CP) = $4310 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 = 220%
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
= 220% of m
= 220% × m
= 220/100 × m
⇒ Profit = 220 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 13792 = m + 220 m/100
⇒ 13792 = 100 m + 220 m/100
⇒ 13792 = 320 m/100
After cross multiplication, we get
13792 × 100 = 320 m
⇒ 320 m = 13792 × 100
⇒ m = 13792 × 100/320
⇒ m = 1379200/320 = 4310
⇒ m = 4310
Thus, the Cost Price (CP) = $4310 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) = $13792
And, the profit = 220%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 220% of 100 = 220
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 220
⇒ Sale Price (SP) = 320
∵ If the Sale Price (SP) is 320, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/320
∴ If the Sale Price (SP) is 13792, then the Cost Price (CP)
= 100/320 × 13792
= 100 × 13792/320
= 1379200/320 = 4310
Thus, the Cost Price (CP) = $4310 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $13792
And, the profit = 220%
Then, the Cost Price (CP) = ?
SP = 320% of CP
⇒ SP = 320/100 × CP
⇒ 13792 = 320 CP/100
After cross multiplication
⇒ 13792 × 100 = 320 CP
⇒ 320 CP = 13792 × 100
⇒ CP = 13792 × 100/320
⇒ CP = 1379200/320 = 4310
⇒ CP = $4310 Answer
Similar Questions
(1) If Robert purchased a TV set in an auction at $250 and sold it at $300, then calculate the profit earned and profit percent in this sale.
(2) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.
(3) Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724
(4) If a trader gets a loss of 66% by selling ten TV sets for $4423.40 then find the cost price of all those TV sets
(5) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80
(6) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?
(7) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?
(8) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?
(9) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?
(10) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?