Question:
A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?
Correct Answer
4227.6
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) = $1165.3
And, the loss = 57%
Then, the Sale Price (SP) to earn a profit of 56% = ?
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 – 57 × 1165.3
= 100/43 × 1165.3
= 100 × 1165.3/43
= 116530/43 = 2710
Thus, the Cost Price (CP) = $2710
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $2710
And, profit = 56%
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 + 56/100 × 2710
= 156/100 × 2710
= 156 × 2710/100
= 422760/100 = 4227.6
Thus, Sale Price (SP) at a profit of 56% = $4227.6 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) = $1165.3
And, the loss = 57%
Then, the Sale Price (SP) to earn a profit of 56% = ?
Let the Cost Price (CP) = m
Here given loss = 57%
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
= 57% of m
= 57% × m
= 57/100 × m
⇒ loss = 57 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1165.3 = m – 57 m/100
⇒ 1165.3 = 100 m – 57 m/100
⇒ 1165.3 = 43 m/100
After cross multiplication, we get
1165.3 × 100 = 43 m
⇒ 43 m = 1165.3 × 100
⇒ m = 1165.3 × 100/43
⇒ m = 116530/43 = 2710
⇒ m = 2710
Thus, the Cost Price (CP) = $2710
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 2710
And, the profit = 56%
Thus, Sale Price (SP)
= Cost Price (CP) + 56% of Cost Price (CP)
= 2710 + 56/100 × 2710
= 2710 + 56 × 2710/100
= 2710 + 151760/100
= 2710 + 1517.6 = 4227.6
Thus, Sale Price (SP) at a profit of 56% = $4227.6 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) = $1165.3
And, the loss = 57%
Then, the Sale Price (SP) to earn a profit of 56% = ?
Let, CP = 100
56% profit = 56% of CP
= 56% of 100 = 56
Thus, Sale Price to earn a profit of 56% = CP + 56
= 100 + 56 = 156
⇒ Sale Price to earn a profit of 56% = 156
57% loss = 57% of CP
= 57% of 100 = 57
Thus, Sale Price at a loss of 57% = CP – Loss
= 100 – 57 = 43
⇒ Sale Price at a loss of 57% = 43
∵ If the Sale Price is 43, then to earn a profit of 56% the Sale Price should be = 156
∴ If the Sale Price is 1, then to earn a profit of 56% the Sale Price should be
= 156/43
∴ If the Sale Price is 1165.3, then to earn a profit of 56% the Sale Price should be
= 156/43 × 1165.3
= 156 × 1165.3/43
= 181786.8/43 = 4227.6
Thus, Sale Price to get a profit of 56% = $4227.6 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) = $1165.3
And, the loss = 57%
Then, the Sale Price (SP) to earn a profit of 56% = ?
Here, the Sale Price at a loss of 57 = $1165.3
This means 43% of the Cost Price (CP) = 1165.3
Therefore, 1% of the Cost Price (CP) = 1165.3/43
Therefore, 100% of the Cost Price (CP)
= 1165.3/43 × 100 = 2710
Thus, the Cost Price (CP) = $2710
Now, we need to find the Sale Price at a profit of 56%
Thus, Sale Price at a profit of 56%
= 156% of the Cost Price (CP)
= 156% of 2710
= 156/100 × 2710 = 4227.6
Thus, the Cost Price at a profit of 56% = $4227.6 Answer
Similar Questions
(1) If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage.
(2) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.
(3) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.
(4) What will be profit percent if a peddler buys 12 kiwis for $1 and sells 11 kiwis for $1?
(5) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90
(6) 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.
(7) A dealer gets a loss of 7% by selling an article for $195.30 then, for how much should he sell it to get a profit of 6%?
(8) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5
(9) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.
(10) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?