Question:
James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?
Correct Answer
5328.6
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) = $1059.3
And, the loss = 67%
Then, the Sale Price (SP) to earn a profit of 66% = ?
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 – 67 × 1059.3
= 100/33 × 1059.3
= 100 × 1059.3/33
= 105930/33 = 3210
Thus, the Cost Price (CP) = $3210
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $3210
And, profit = 66%
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 + 66/100 × 3210
= 166/100 × 3210
= 166 × 3210/100
= 532860/100 = 5328.6
Thus, Sale Price (SP) at a profit of 66% = $5328.6 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) = $1059.3
And, the loss = 67%
Then, the Sale Price (SP) to earn a profit of 66% = ?
Let the Cost Price (CP) = m
Here given loss = 67%
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
= 67% of m
= 67% × m
= 67/100 × m
⇒ loss = 67 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1059.3 = m – 67 m/100
⇒ 1059.3 = 100 m – 67 m/100
⇒ 1059.3 = 33 m/100
After cross multiplication, we get
1059.3 × 100 = 33 m
⇒ 33 m = 1059.3 × 100
⇒ m = 1059.3 × 100/33
⇒ m = 105930/33 = 3210
⇒ m = 3210
Thus, the Cost Price (CP) = $3210
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 3210
And, the profit = 66%
Thus, Sale Price (SP)
= Cost Price (CP) + 66% of Cost Price (CP)
= 3210 + 66/100 × 3210
= 3210 + 66 × 3210/100
= 3210 + 211860/100
= 3210 + 2118.6 = 5328.6
Thus, Sale Price (SP) at a profit of 66% = $5328.6 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) = $1059.3
And, the loss = 67%
Then, the Sale Price (SP) to earn a profit of 66% = ?
Let, CP = 100
66% profit = 66% of CP
= 66% of 100 = 66
Thus, Sale Price to earn a profit of 66% = CP + 66
= 100 + 66 = 166
⇒ Sale Price to earn a profit of 66% = 166
67% loss = 67% of CP
= 67% of 100 = 67
Thus, Sale Price at a loss of 67% = CP – Loss
= 100 – 67 = 33
⇒ Sale Price at a loss of 67% = 33
∵ If the Sale Price is 33, then to earn a profit of 66% the Sale Price should be = 166
∴ If the Sale Price is 1, then to earn a profit of 66% the Sale Price should be
= 166/33
∴ If the Sale Price is 1059.3, then to earn a profit of 66% the Sale Price should be
= 166/33 × 1059.3
= 166 × 1059.3/33
= 175843.8/33 = 5328.6
Thus, Sale Price to get a profit of 66% = $5328.6 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) = $1059.3
And, the loss = 67%
Then, the Sale Price (SP) to earn a profit of 66% = ?
Here, the Sale Price at a loss of 67 = $1059.3
This means 33% of the Cost Price (CP) = 1059.3
Therefore, 1% of the Cost Price (CP) = 1059.3/33
Therefore, 100% of the Cost Price (CP)
= 1059.3/33 × 100 = 3210
Thus, the Cost Price (CP) = $3210
Now, we need to find the Sale Price at a profit of 66%
Thus, Sale Price at a profit of 66%
= 166% of the Cost Price (CP)
= 166% of 3210
= 166/100 × 3210 = 5328.6
Thus, the Cost Price at a profit of 66% = $5328.6 Answer
Similar Questions
(1) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.
(2) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?
(3) To earn a profit of 7% Mr. Robert should sell his article for how much if he gets a loss of 8% by selling it for $239.20?
(4) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.
(5) Find the cost price, if a broker earns a profit of 370% by selling an old house for $34357
(6) Find the cost price, if a trader gets a loss of 35% by selling some articles for $4426.50
(7) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.
(8) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.
(9) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.
(10) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.