Profit And Loss
Math MCQs

Question :    Potter loses 90% by selling an article for $436. For how much should he sell it to get a profit of 89%?

Correct Answer  8240.4

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) = $436

And, the loss = 90%

Then, the Sale Price (SP) to earn a profit of 89% = ?

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 – 90} × 436

= ¹⁰⁰/₁₀ × 436

= ^{100 × 436}/₁₀

= ⁴³⁶⁰⁰/₁₀ = 4360

Thus, the Cost Price (CP) = $4360

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

Here now, CP = $4360

And, profit = 89%

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 + 89}/₁₀₀ × 4360

= ¹⁸⁹/₁₀₀ × 4360

= ^{189 × 4360}/₁₀₀

= ⁸²⁴⁰⁴⁰/₁₀₀ = 8240.4

Thus, Sale Price (SP) at a profit of 89% = $8240.4 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) = $436

And, the loss = 90%

Then, the Sale Price (SP) to earn a profit of 89% = ?

Let the Cost Price (CP) = m

Here given loss = 90%

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

= 90% of m

= 90% × m

= ⁹⁰/₁₀₀ × m

⇒ loss = ^{90 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 436 = m – ^{90 m}/₁₀₀

⇒ 436 = ^{100 m – 90 m}/₁₀₀

⇒ 436 = ^{10 m}/₁₀₀

After cross multiplication, we get

436 × 100 = 10 m

⇒ 10 m = 436 × 100

⇒ m = ^{436 × 100}/₁₀

⇒ m = ⁴³⁶⁰⁰/₁₀ = 4360

⇒ m = 4360

Thus, the Cost Price (CP) = $4360

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

Now, here, Cost Price = 4360

And, the profit = 89%

Thus, Sale Price (SP)

= Cost Price (CP) + 89% of Cost Price (CP)

= 4360 + ⁸⁹/₁₀₀ × 4360

= 4360 + ^{89 × 4360}/₁₀₀

= 4360 + ³⁸⁸⁰⁴⁰/₁₀₀

= 4360 + 3880.4 = 8240.4

Thus, Sale Price (SP) at a profit of 89% = $8240.4 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) = $436

And, the loss = 90%

Then, the Sale Price (SP) to earn a profit of 89% = ?

Let, CP = 100

89% profit = 89% of CP

= 89% of 100 = 89

Thus, Sale Price to earn a profit of 89% = CP + 89

= 100 + 89 = 189

⇒ Sale Price to earn a profit of 89% = 189

90% loss = 90% of CP

= 90% of 100 = 90

Thus, Sale Price at a loss of 90% = CP – Loss

= 100 – 90 = 10

⇒ Sale Price at a loss of 90% = 10

∵ If the Sale Price is 10, then to earn a profit of 89% the Sale Price should be = 189

∴ If the Sale Price is 1, then to earn a profit of 89% the Sale Price should be

= ¹⁸⁹/₁₀

∴ If the Sale Price is 436, then to earn a profit of 89% the Sale Price should be

= ¹⁸⁹/₁₀ × 436

= ^{189 × 436}/₁₀

= ⁸²⁴⁰⁴/₁₀ = 8240.4

Thus, Sale Price to get a profit of 89% = $8240.4 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) = $436

And, the loss = 90%

Then, the Sale Price (SP) to earn a profit of 89% = ?

Here, the Sale Price at a loss of 90 = $436

This means 10% of the Cost Price (CP) = 436

Therefore, 1% of the Cost Price (CP) = ⁴³⁶/₁₀

Therefore, 100% of the Cost Price (CP)

= ⁴³⁶/₁₀ × 100 = 4360

Thus, the Cost Price (CP) = $4360

Now, we need to find the Sale Price at a profit of 89%

Thus, Sale Price at a profit of 89%

= 189% of the Cost Price (CP)

= 189% of 4360

= ¹⁸⁹/₁₀₀ × 4360 = 8240.4

Thus, the Cost Price at a profit of 89% = $8240.4 Answer

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