Profit And Loss
Math MCQs

Question :    William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

Correct Answer  5797

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) = $988.9

And, the loss = 71%

Then, the Sale Price (SP) to earn a profit of 70% = ?

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 – 71} × 988.9

= ¹⁰⁰/₂₉ × 988.9

= ^{100 × 988.9}/₂₉

= ⁹⁸⁸⁹⁰/₂₉ = 3410

Thus, the Cost Price (CP) = $3410

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

Here now, CP = $3410

And, profit = 70%

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 + 70}/₁₀₀ × 3410

= ¹⁷⁰/₁₀₀ × 3410

= ^{170 × 3410}/₁₀₀

= ⁵⁷⁹⁷⁰⁰/₁₀₀ = 5797

Thus, Sale Price (SP) at a profit of 70% = $5797 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) = $988.9

And, the loss = 71%

Then, the Sale Price (SP) to earn a profit of 70% = ?

Let the Cost Price (CP) = m

Here given loss = 71%

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

= 71% of m

= 71% × m

= ⁷¹/₁₀₀ × m

⇒ loss = ^{71 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 988.9 = m – ^{71 m}/₁₀₀

⇒ 988.9 = ^{100 m – 71 m}/₁₀₀

⇒ 988.9 = ^{29 m}/₁₀₀

After cross multiplication, we get

988.9 × 100 = 29 m

⇒ 29 m = 988.9 × 100

⇒ m = ^{988.9 × 100}/₂₉

⇒ m = ⁹⁸⁸⁹⁰/₂₉ = 3410

⇒ m = 3410

Thus, the Cost Price (CP) = $3410

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

Now, here, Cost Price = 3410

And, the profit = 70%

Thus, Sale Price (SP)

= Cost Price (CP) + 70% of Cost Price (CP)

= 3410 + ⁷⁰/₁₀₀ × 3410

= 3410 + ^{70 × 3410}/₁₀₀

= 3410 + ²³⁸⁷⁰⁰/₁₀₀

= 3410 + 2387 = 5797

Thus, Sale Price (SP) at a profit of 70% = $5797 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) = $988.9

And, the loss = 71%

Then, the Sale Price (SP) to earn a profit of 70% = ?

Let, CP = 100

70% profit = 70% of CP

= 70% of 100 = 70

Thus, Sale Price to earn a profit of 70% = CP + 70

= 100 + 70 = 170

⇒ Sale Price to earn a profit of 70% = 170

71% loss = 71% of CP

= 71% of 100 = 71

Thus, Sale Price at a loss of 71% = CP – Loss

= 100 – 71 = 29

⇒ Sale Price at a loss of 71% = 29

∵ If the Sale Price is 29, then to earn a profit of 70% the Sale Price should be = 170

∴ If the Sale Price is 1, then to earn a profit of 70% the Sale Price should be

= ¹⁷⁰/₂₉

∴ If the Sale Price is 988.9, then to earn a profit of 70% the Sale Price should be

= ¹⁷⁰/₂₉ × 988.9

= ^{170 × 988.9}/₂₉

= ¹⁶⁸¹¹³/₂₉ = 5797

Thus, Sale Price to get a profit of 70% = $5797 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) = $988.9

And, the loss = 71%

Then, the Sale Price (SP) to earn a profit of 70% = ?

Here, the Sale Price at a loss of 71 = $988.9

This means 29% of the Cost Price (CP) = 988.9

Therefore, 1% of the Cost Price (CP) = ^988.9/₂₉

Therefore, 100% of the Cost Price (CP)

= ^988.9/₂₉ × 100 = 3410

Thus, the Cost Price (CP) = $3410

Now, we need to find the Sale Price at a profit of 70%

Thus, Sale Price at a profit of 70%

= 170% of the Cost Price (CP)

= 170% of 3410

= ¹⁷⁰/₁₀₀ × 3410 = 5797

Thus, the Cost Price at a profit of 70% = $5797 Answer

Similar Questions

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