Profit And Loss
Math MCQs

Question :    Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

Correct Answer  451

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) = $364.9

And, the loss = 11%

Then, the Sale Price (SP) to earn a profit of 10% = ?

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 – 11} × 364.9

= ¹⁰⁰/₈₉ × 364.9

= ^{100 × 364.9}/₈₉

= ³⁶⁴⁹⁰/₈₉ = 410

Thus, the Cost Price (CP) = $410

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

Here now, CP = $410

And, profit = 10%

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 + 10}/₁₀₀ × 410

= ¹¹⁰/₁₀₀ × 410

= ^{110 × 410}/₁₀₀

= ⁴⁵¹⁰⁰/₁₀₀ = 451

Thus, Sale Price (SP) at a profit of 10% = $451 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) = $364.9

And, the loss = 11%

Then, the Sale Price (SP) to earn a profit of 10% = ?

Let the Cost Price (CP) = m

Here given loss = 11%

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

= 11% of m

= 11% × m

= ¹¹/₁₀₀ × m

⇒ loss = ^{11 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 364.9 = m – ^{11 m}/₁₀₀

⇒ 364.9 = ^{100 m – 11 m}/₁₀₀

⇒ 364.9 = ^{89 m}/₁₀₀

After cross multiplication, we get

364.9 × 100 = 89 m

⇒ 89 m = 364.9 × 100

⇒ m = ^{364.9 × 100}/₈₉

⇒ m = ³⁶⁴⁹⁰/₈₉ = 410

⇒ m = 410

Thus, the Cost Price (CP) = $410

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

Now, here, Cost Price = 410

And, the profit = 10%

Thus, Sale Price (SP)

= Cost Price (CP) + 10% of Cost Price (CP)

= 410 + ¹⁰/₁₀₀ × 410

= 410 + ^{10 × 410}/₁₀₀

= 410 + ⁴¹⁰⁰/₁₀₀

= 410 + 41 = 451

Thus, Sale Price (SP) at a profit of 10% = $451 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) = $364.9

And, the loss = 11%

Then, the Sale Price (SP) to earn a profit of 10% = ?

Let, CP = 100

10% profit = 10% of CP

= 10% of 100 = 10

Thus, Sale Price to earn a profit of 10% = CP + 10

= 100 + 10 = 110

⇒ Sale Price to earn a profit of 10% = 110

11% loss = 11% of CP

= 11% of 100 = 11

Thus, Sale Price at a loss of 11% = CP – Loss

= 100 – 11 = 89

⇒ Sale Price at a loss of 11% = 89

∵ If the Sale Price is 89, then to earn a profit of 10% the Sale Price should be = 110

∴ If the Sale Price is 1, then to earn a profit of 10% the Sale Price should be

= ¹¹⁰/₈₉

∴ If the Sale Price is 364.9, then to earn a profit of 10% the Sale Price should be

= ¹¹⁰/₈₉ × 364.9

= ^{110 × 364.9}/₈₉

= ⁴⁰¹³⁹/₈₉ = 451

Thus, Sale Price to get a profit of 10% = $451 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) = $364.9

And, the loss = 11%

Then, the Sale Price (SP) to earn a profit of 10% = ?

Here, the Sale Price at a loss of 11 = $364.9

This means 89% of the Cost Price (CP) = 364.9

Therefore, 1% of the Cost Price (CP) = ^364.9/₈₉

Therefore, 100% of the Cost Price (CP)

= ^364.9/₈₉ × 100 = 410

Thus, the Cost Price (CP) = $410

Now, we need to find the Sale Price at a profit of 10%

Thus, Sale Price at a profit of 10%

= 110% of the Cost Price (CP)

= 110% of 410

= ¹¹⁰/₁₀₀ × 410 = 451

Thus, the Cost Price at a profit of 10% = $451 Answer

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