Question:
Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718
Correct Answer
1510
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) = $2718
And, the profit = 80%
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 + 80 × 2718
= 100 × 2718/180
= 271800/180 = 1510
Thus, the Cost Price (CP) = $1510 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 = 80%
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
= 80% of m
= 80% × m
= 80/100 × m
⇒ Profit = 80 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 2718 = m + 80 m/100
⇒ 2718 = 100 m + 80 m/100
⇒ 2718 = 180 m/100
After cross multiplication, we get
2718 × 100 = 180 m
⇒ 180 m = 2718 × 100
⇒ m = 2718 × 100/180
⇒ m = 271800/180 = 1510
⇒ m = 1510
Thus, the Cost Price (CP) = $1510 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) = $2718
And, the profit = 80%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 80% of 100 = 80
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 80
⇒ Sale Price (SP) = 180
∵ If the Sale Price (SP) is 180, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/180
∴ If the Sale Price (SP) is 2718, then the Cost Price (CP)
= 100/180 × 2718
= 100 × 2718/180
= 271800/180 = 1510
Thus, the Cost Price (CP) = $1510 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $2718
And, the profit = 80%
Then, the Cost Price (CP) = ?
SP = 180% of CP
⇒ SP = 180/100 × CP
⇒ 2718 = 180 CP/100
After cross multiplication
⇒ 2718 × 100 = 180 CP
⇒ 180 CP = 2718 × 100
⇒ CP = 2718 × 100/180
⇒ CP = 271800/180 = 1510
⇒ CP = $1510 Answer
Similar Questions
(1) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.
(2) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.
(3) The cost price of an article is $12, and the sale price is $15. Find the profit and profit percent.
(4) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?
(5) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90
(6) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?
(7) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.
(8) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?
(9) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?
(10) A trader loses 55% by selling an article for $1174.50. For how much should he sell it to get a profit of 54%?