Question:
A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?
Correct Answer
3418.8
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) = $1178.1
And, the loss = 49%
Then, the Sale Price (SP) to earn a profit of 48% = ?
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 – 49 × 1178.1
= 100/51 × 1178.1
= 100 × 1178.1/51
= 117810/51 = 2310
Thus, the Cost Price (CP) = $2310
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $2310
And, profit = 48%
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 + 48/100 × 2310
= 148/100 × 2310
= 148 × 2310/100
= 341880/100 = 3418.8
Thus, Sale Price (SP) at a profit of 48% = $3418.8 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) = $1178.1
And, the loss = 49%
Then, the Sale Price (SP) to earn a profit of 48% = ?
Let the Cost Price (CP) = m
Here given loss = 49%
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
= 49% of m
= 49% × m
= 49/100 × m
⇒ loss = 49 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1178.1 = m – 49 m/100
⇒ 1178.1 = 100 m – 49 m/100
⇒ 1178.1 = 51 m/100
After cross multiplication, we get
1178.1 × 100 = 51 m
⇒ 51 m = 1178.1 × 100
⇒ m = 1178.1 × 100/51
⇒ m = 117810/51 = 2310
⇒ m = 2310
Thus, the Cost Price (CP) = $2310
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 2310
And, the profit = 48%
Thus, Sale Price (SP)
= Cost Price (CP) + 48% of Cost Price (CP)
= 2310 + 48/100 × 2310
= 2310 + 48 × 2310/100
= 2310 + 110880/100
= 2310 + 1108.8 = 3418.8
Thus, Sale Price (SP) at a profit of 48% = $3418.8 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) = $1178.1
And, the loss = 49%
Then, the Sale Price (SP) to earn a profit of 48% = ?
Let, CP = 100
48% profit = 48% of CP
= 48% of 100 = 48
Thus, Sale Price to earn a profit of 48% = CP + 48
= 100 + 48 = 148
⇒ Sale Price to earn a profit of 48% = 148
49% loss = 49% of CP
= 49% of 100 = 49
Thus, Sale Price at a loss of 49% = CP – Loss
= 100 – 49 = 51
⇒ Sale Price at a loss of 49% = 51
∵ If the Sale Price is 51, then to earn a profit of 48% the Sale Price should be = 148
∴ If the Sale Price is 1, then to earn a profit of 48% the Sale Price should be
= 148/51
∴ If the Sale Price is 1178.1, then to earn a profit of 48% the Sale Price should be
= 148/51 × 1178.1
= 148 × 1178.1/51
= 174358.8/51 = 3418.8
Thus, Sale Price to get a profit of 48% = $3418.8 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) = $1178.1
And, the loss = 49%
Then, the Sale Price (SP) to earn a profit of 48% = ?
Here, the Sale Price at a loss of 49 = $1178.1
This means 51% of the Cost Price (CP) = 1178.1
Therefore, 1% of the Cost Price (CP) = 1178.1/51
Therefore, 100% of the Cost Price (CP)
= 1178.1/51 × 100 = 2310
Thus, the Cost Price (CP) = $2310
Now, we need to find the Sale Price at a profit of 48%
Thus, Sale Price at a profit of 48%
= 148% of the Cost Price (CP)
= 148% of 2310
= 148/100 × 2310 = 3418.8
Thus, the Cost Price at a profit of 48% = $3418.8 Answer
Similar Questions
(1) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.
(2) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?
(3) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?
(4) Find the cost price, if a trader gets a loss of 69% by selling 12 bags of fruit for $4219.10
(5) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?
(6) Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.
(7) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.
(8) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?
(9) Find the cost price, if a trader gets a loss of 45% by selling 800 bags of fruits for $4845.50
(10) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?