Profit And Loss
Math MCQs

Question :    Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?

Correct Answer  6909.4

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) = $772

And, the loss = 80%

Then, the Sale Price (SP) to earn a profit of 79% = ?

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 – 80} × 772

= ¹⁰⁰/₂₀ × 772

= ^{100 × 772}/₂₀

= ⁷⁷²⁰⁰/₂₀ = 3860

Thus, the Cost Price (CP) = $3860

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

Here now, CP = $3860

And, profit = 79%

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 + 79}/₁₀₀ × 3860

= ¹⁷⁹/₁₀₀ × 3860

= ^{179 × 3860}/₁₀₀

= ⁶⁹⁰⁹⁴⁰/₁₀₀ = 6909.4

Thus, Sale Price (SP) at a profit of 79% = $6909.4 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) = $772

And, the loss = 80%

Then, the Sale Price (SP) to earn a profit of 79% = ?

Let the Cost Price (CP) = m

Here given loss = 80%

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

= 80% of m

= 80% × m

= ⁸⁰/₁₀₀ × m

⇒ loss = ^{80 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 772 = m – ^{80 m}/₁₀₀

⇒ 772 = ^{100 m – 80 m}/₁₀₀

⇒ 772 = ^{20 m}/₁₀₀

After cross multiplication, we get

772 × 100 = 20 m

⇒ 20 m = 772 × 100

⇒ m = ^{772 × 100}/₂₀

⇒ m = ⁷⁷²⁰⁰/₂₀ = 3860

⇒ m = 3860

Thus, the Cost Price (CP) = $3860

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

Now, here, Cost Price = 3860

And, the profit = 79%

Thus, Sale Price (SP)

= Cost Price (CP) + 79% of Cost Price (CP)

= 3860 + ⁷⁹/₁₀₀ × 3860

= 3860 + ^{79 × 3860}/₁₀₀

= 3860 + ³⁰⁴⁹⁴⁰/₁₀₀

= 3860 + 3049.4 = 6909.4

Thus, Sale Price (SP) at a profit of 79% = $6909.4 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) = $772

And, the loss = 80%

Then, the Sale Price (SP) to earn a profit of 79% = ?

Let, CP = 100

79% profit = 79% of CP

= 79% of 100 = 79

Thus, Sale Price to earn a profit of 79% = CP + 79

= 100 + 79 = 179

⇒ Sale Price to earn a profit of 79% = 179

80% loss = 80% of CP

= 80% of 100 = 80

Thus, Sale Price at a loss of 80% = CP – Loss

= 100 – 80 = 20

⇒ Sale Price at a loss of 80% = 20

∵ If the Sale Price is 20, then to earn a profit of 79% the Sale Price should be = 179

∴ If the Sale Price is 1, then to earn a profit of 79% the Sale Price should be

= ¹⁷⁹/₂₀

∴ If the Sale Price is 772, then to earn a profit of 79% the Sale Price should be

= ¹⁷⁹/₂₀ × 772

= ^{179 × 772}/₂₀

= ¹³⁸¹⁸⁸/₂₀ = 6909.4

Thus, Sale Price to get a profit of 79% = $6909.4 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) = $772

And, the loss = 80%

Then, the Sale Price (SP) to earn a profit of 79% = ?

Here, the Sale Price at a loss of 80 = $772

This means 20% of the Cost Price (CP) = 772

Therefore, 1% of the Cost Price (CP) = ⁷⁷²/₂₀

Therefore, 100% of the Cost Price (CP)

= ⁷⁷²/₂₀ × 100 = 3860

Thus, the Cost Price (CP) = $3860

Now, we need to find the Sale Price at a profit of 79%

Thus, Sale Price at a profit of 79%

= 179% of the Cost Price (CP)

= 179% of 3860

= ¹⁷⁹/₁₀₀ × 3860 = 6909.4

Thus, the Cost Price at a profit of 79% = $6909.4 Answer

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