Question:
Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?
Correct Answer
2157.4
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) = $1046.5
And, the loss = 35%
Then, the Sale Price (SP) to earn a profit of 34% = ?
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 – 35 × 1046.5
= 100/65 × 1046.5
= 100 × 1046.5/65
= 104650/65 = 1610
Thus, the Cost Price (CP) = $1610
Finding the Sale Price using the formula when the cost price and Profit percent are known
Here now, CP = $1610
And, profit = 34%
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 + 34/100 × 1610
= 134/100 × 1610
= 134 × 1610/100
= 215740/100 = 2157.4
Thus, Sale Price (SP) at a profit of 34% = $2157.4 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) = $1046.5
And, the loss = 35%
Then, the Sale Price (SP) to earn a profit of 34% = ?
Let the Cost Price (CP) = m
Here given loss = 35%
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
= 35% of m
= 35% × m
= 35/100 × m
⇒ loss = 35 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) – loss
⇒ 1046.5 = m – 35 m/100
⇒ 1046.5 = 100 m – 35 m/100
⇒ 1046.5 = 65 m/100
After cross multiplication, we get
1046.5 × 100 = 65 m
⇒ 65 m = 1046.5 × 100
⇒ m = 1046.5 × 100/65
⇒ m = 104650/65 = 1610
⇒ m = 1610
Thus, the Cost Price (CP) = $1610
Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known
Now, here, Cost Price = 1610
And, the profit = 34%
Thus, Sale Price (SP)
= Cost Price (CP) + 34% of Cost Price (CP)
= 1610 + 34/100 × 1610
= 1610 + 34 × 1610/100
= 1610 + 54740/100
= 1610 + 547.4 = 2157.4
Thus, Sale Price (SP) at a profit of 34% = $2157.4 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) = $1046.5
And, the loss = 35%
Then, the Sale Price (SP) to earn a profit of 34% = ?
Let, CP = 100
34% profit = 34% of CP
= 34% of 100 = 34
Thus, Sale Price to earn a profit of 34% = CP + 34
= 100 + 34 = 134
⇒ Sale Price to earn a profit of 34% = 134
35% loss = 35% of CP
= 35% of 100 = 35
Thus, Sale Price at a loss of 35% = CP – Loss
= 100 – 35 = 65
⇒ Sale Price at a loss of 35% = 65
∵ If the Sale Price is 65, then to earn a profit of 34% the Sale Price should be = 134
∴ If the Sale Price is 1, then to earn a profit of 34% the Sale Price should be
= 134/65
∴ If the Sale Price is 1046.5, then to earn a profit of 34% the Sale Price should be
= 134/65 × 1046.5
= 134 × 1046.5/65
= 140231/65 = 2157.4
Thus, Sale Price to get a profit of 34% = $2157.4 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) = $1046.5
And, the loss = 35%
Then, the Sale Price (SP) to earn a profit of 34% = ?
Here, the Sale Price at a loss of 35 = $1046.5
This means 65% of the Cost Price (CP) = 1046.5
Therefore, 1% of the Cost Price (CP) = 1046.5/65
Therefore, 100% of the Cost Price (CP)
= 1046.5/65 × 100 = 1610
Thus, the Cost Price (CP) = $1610
Now, we need to find the Sale Price at a profit of 34%
Thus, Sale Price at a profit of 34%
= 134% of the Cost Price (CP)
= 134% of 1610
= 134/100 × 1610 = 2157.4
Thus, the Cost Price at a profit of 34% = $2157.4 Answer
Similar Questions
(1) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7
(2) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?
(3) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.
(4) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?
(5) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.
(6) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?
(7) Find the cost price, if a trader gets a loss of 41% by selling an article for $4725.90
(8) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?
(9) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?
(10) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.