Question:
A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?
Correct Answer
2585.4
Solution And Explanation
Strategy to solve the question
Step (1) Calculate the cost price at given loss percent and the sale price.
Step (2) After gettting the cost price find the sale price at given profit percent.
Solution
Method (1) Formula Method
Finding the Sale Price to earn a profit using formula when the Sale Price at a loss is given
Given, the sale price (SP) = $1116
And, the loss = 40%
Then, the Sale Price (SP) to earn a profit of 39% = ?
Formula to find the cost price when the sale price and loss percent are known
Cost Price (CP) = 100/100 – gain% × SP
Thus, the Cost Price (CP)
= 100/100 – 40 × 1116
= 100/60 × 1116
= 100 × 1116/60
= 111600/60 = 1860
Thus, the Cost Price (CP) = $1860
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $1860
And, profit = 39%
Thus Sale Price (SP) = ?
Formula to find the Sale Price (SP) when the cost price (CP) and profit percent are known
Sale Price (SP) = 100 + gain%/100 × Cost Price (CP)
Thus, the Sale Price (SP)
= 100 + 39/100 × 1860
= 139/100 × 1860
= 139 × 1860/100
= 258540/100 = 2585.4
Thus, Sale Price (SP) at a profit of 39% = $2585.4 Answer
Method (2) Algebraic Method
Finding the Sale Price (SP) to earn the given profit using the Algebraic Method when the Sale Pric (SP) at a loss percent is given
Given, the sale price (SP) = $1116
And, the loss = 40%
Then, the Sale Price (SP) to earn a profit of 39% = ?
Let the Cost Price (CP) = m
Here given loss = 40%
Calculation of loss
loss is calculated on cost price (CP)
Formula to find the loss = loss% of CP
Thus, loss on the cost price of m
= 40% of m
= 40% × m
= 40/100 × m
⇒ loss = 40 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1116 = m – 40 m/100
⇒ 1116 = 100 m – 40 m/100
⇒ 1116 = 60 m/100
After cross multiplication, we get
1116 × 100 = 60 m
⇒ 60 m = 1116 × 100
⇒ m = 1116 × 100/60
⇒ m = 111600/60 = 1860
⇒ m = 1860
Thus, the Cost Price (CP) = $1860
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 1860
And, the profit = 39%
Thus, Sale Price (SP)
= Cost Price (CP) + 39% of Cost Price (CP)
= 1860 + 39/100 × 1860
= 1860 + 39 × 1860/100
= 1860 + 72540/100
= 1860 + 725.4 = 2585.4
Thus, Sale Price (SP) at a profit of 39% = $2585.4 Answer
Method (3) Unitary Method
Finding the Sale Price (SP) to earn a given profit when the Sale price (SP) at a loss is given
Given, the sale price (SP) = $1116
And, the loss = 40%
Then, the Sale Price (SP) to earn a profit of 39% = ?
Let, CP = 100
39% profit = 39% of CP
= 39% of 100 = 39
Thus, Sale Price to earn a profit of 39% = CP + 39
= 100 + 39 = 139
⇒ Sale Price to earn a profit of 39% = 139
40% loss = 40% of CP
= 40% of 100 = 40
Thus, Sale Price at a loss of 40% = CP – Loss
= 100 – 40 = 60
⇒ Sale Price at a loss of 40% = 60
∵ If the Sale Price is 60, then to earn a profit of 39% the Sale Price should be = 139
∴ If the Sale Price is 1, then to earn a profit of 39% the Sale Price should be
= 139/60
∴ If the Sale Price is 1116, then to earn a profit of 39% the Sale Price should be
= 139/60 × 1116
= 139 × 1116/60
= 155124/60 = 2585.4
Thus, Sale Price to get a profit of 39% = $2585.4 Answer
Method (4) Shortcut Method
Shortcut Method to find the Sale Price at a given profit when Sale Price at a loss is given
Given, the sale price (SP) = $1116
And, the loss = 40%
Then, the Sale Price (SP) to earn a profit of 39% = ?
Here, the Sale Price at a loss of 40 = $1116
This means 60% of the Cost Price (CP) = 1116
Therefore, 1% of the Cost Price (CP) = 1116/60
Therefore, 100% of the Cost Price (CP)
= 1116/60 × 100 = 1860
Thus, the Cost Price (CP) = $1860
Now, we need to find the Sale Price at a profit of 39%
Thus, Sale Price at a profit of 39%
= 139% of the Cost Price (CP)
= 139% of 1860
= 139/100 × 1860 = 2585.4
Thus, the Cost Price at a profit of 39% = $2585.4 Answer
Similar Questions
(1) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?
(2) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.
(3) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?
(4) If a trader gets a loss of 4% by selling an article for $585.60 then, find the cost price.
(5) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.
(6) Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.
(7) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?
(8) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.
(9) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.
(10) If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.