Profit And Loss
Math MCQs

Question :    Mrs. Jolly loses 18% by selling an article for $623.20. For how much should she sell it to get a profit of 17%?

Correct Answer  889.2

Solution & 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) = $623.2

And, the loss = 18%

Then, the Sale Price (SP) to earn a profit of 17% = ?

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 – 18} × 623.2

= ¹⁰⁰/₈₂ × 623.2

= ^{100 × 623.2}/₈₂

= ⁶²³²⁰/₈₂ = 760

Thus, the Cost Price (CP) = $760

Finding the Sale Price using the formula when the cost price and Profit percent are known

Here now, CP = $760

And, profit = 17%

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 + 17}/₁₀₀ × 760

= ¹¹⁷/₁₀₀ × 760

= ^{117 × 760}/₁₀₀

= ⁸⁸⁹²⁰/₁₀₀ = 889.2

Thus, Sale Price (SP) at a profit of 17% = $889.2 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) = $623.2

And, the loss = 18%

Then, the Sale Price (SP) to earn a profit of 17% = ?

Let the Cost Price (CP) = m

Here given loss = 18%

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

= 18% of m

= 18% × m

= ¹⁸/₁₀₀ × m

⇒ loss = ^{18 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) – loss

⇒ 623.2 = m – ^{18 m}/₁₀₀

⇒ 623.2 = ^{100 m – 18 m}/₁₀₀

⇒ 623.2 = ^{82 m}/₁₀₀

After cross multiplication, we get

623.2 × 100 = 82 m

⇒ 82 m = 623.2 × 100

⇒ m = ^{623.2 × 100}/₈₂

⇒ m = ⁶²³²⁰/₈₂ = 760

⇒ m = 760

Thus, the Cost Price (CP) = $760

Finding the Sale Price (SP) when the Cost Price (CP) and profit percent are known

Now, here, Cost Price = 760

And, the profit = 17%

Thus, Sale Price (SP)

= Cost Price (CP) + 17% of Cost Price (CP)

= 760 + ¹⁷/₁₀₀ × 760

= 760 + ^{17 × 760}/₁₀₀

= 760 + ¹²⁹²⁰/₁₀₀

= 760 + 129.2 = 889.2

Thus, Sale Price (SP) at a profit of 17% = $889.2 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) = $623.2

And, the loss = 18%

Then, the Sale Price (SP) to earn a profit of 17% = ?

Let, CP = 100

17% profit = 17% of CP

= 17% of 100 = 17

Thus, Sale Price to earn a profit of 17% = CP + 17

= 100 + 17 = 117

⇒ Sale Price to earn a profit of 17% = 117

18% loss = 18% of CP

= 18% of 100 = 18

Thus, Sale Price at a loss of 18% = CP – Loss

= 100 – 18 = 82

⇒ Sale Price at a loss of 18% = 82

∵ If the Sale Price is 82, then to earn a profit of 17% the Sale Price should be = 117

∴ If the Sale Price is 1, then to earn a profit of 17% the Sale Price should be

= ¹¹⁷/₈₂

∴ If the Sale Price is 623.2, then to earn a profit of 17% the Sale Price should be

= ¹¹⁷/₈₂ × 623.2

= ^{117 × 623.2}/₈₂

= ^72914.4/₈₂ = 889.2

Thus, Sale Price to get a profit of 17% = $889.2 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) = $623.2

And, the loss = 18%

Then, the Sale Price (SP) to earn a profit of 17% = ?

Here, the Sale Price at a loss of 18 = $623.2

This means 82% of the Cost Price (CP) = 623.2

Therefore, 1% of the Cost Price (CP) = ^623.2/₈₂

Therefore, 100% of the Cost Price (CP)

= ^623.2/₈₂ × 100 = 760

Thus, the Cost Price (CP) = $760

Now, we need to find the Sale Price at a profit of 17%

Thus, Sale Price at a profit of 17%

= 117% of the Cost Price (CP)

= 117% of 760

= ¹¹⁷/₁₀₀ × 760 = 889.2

Thus, the Cost Price at a profit of 17% = $889.2 Answer

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