Profit And Loss
Math MCQs

Question :    To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?

Correct Answer  759

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) = $554.4

And, the loss = 16%

Then, the Sale Price (SP) to earn a profit of 15% = ?

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 – 16} × 554.4

= ¹⁰⁰/₈₄ × 554.4

= ^{100 × 554.4}/₈₄

= ⁵⁵⁴⁴⁰/₈₄ = 660

Thus, the Cost Price (CP) = $660

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

Here now, CP = $660

And, profit = 15%

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 + 15}/₁₀₀ × 660

= ¹¹⁵/₁₀₀ × 660

= ^{115 × 660}/₁₀₀

= ⁷⁵⁹⁰⁰/₁₀₀ = 759

Thus, Sale Price (SP) at a profit of 15% = $759 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) = $554.4

And, the loss = 16%

Then, the Sale Price (SP) to earn a profit of 15% = ?

Let the Cost Price (CP) = m

Here given loss = 16%

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

= 16% of m

= 16% × m

= ¹⁶/₁₀₀ × m

⇒ loss = ^{16 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 554.4 = m – ^{16 m}/₁₀₀

⇒ 554.4 = ^{100 m – 16 m}/₁₀₀

⇒ 554.4 = ^{84 m}/₁₀₀

After cross multiplication, we get

554.4 × 100 = 84 m

⇒ 84 m = 554.4 × 100

⇒ m = ^{554.4 × 100}/₈₄

⇒ m = ⁵⁵⁴⁴⁰/₈₄ = 660

⇒ m = 660

Thus, the Cost Price (CP) = $660

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

Now, here, Cost Price = 660

And, the profit = 15%

Thus, Sale Price (SP)

= Cost Price (CP) + 15% of Cost Price (CP)

= 660 + ¹⁵/₁₀₀ × 660

= 660 + ^{15 × 660}/₁₀₀

= 660 + ⁹⁹⁰⁰/₁₀₀

= 660 + 99 = 759

Thus, Sale Price (SP) at a profit of 15% = $759 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) = $554.4

And, the loss = 16%

Then, the Sale Price (SP) to earn a profit of 15% = ?

Let, CP = 100

15% profit = 15% of CP

= 15% of 100 = 15

Thus, Sale Price to earn a profit of 15% = CP + 15

= 100 + 15 = 115

⇒ Sale Price to earn a profit of 15% = 115

16% loss = 16% of CP

= 16% of 100 = 16

Thus, Sale Price at a loss of 16% = CP – Loss

= 100 – 16 = 84

⇒ Sale Price at a loss of 16% = 84

∵ If the Sale Price is 84, then to earn a profit of 15% the Sale Price should be = 115

∴ If the Sale Price is 1, then to earn a profit of 15% the Sale Price should be

= ¹¹⁵/₈₄

∴ If the Sale Price is 554.4, then to earn a profit of 15% the Sale Price should be

= ¹¹⁵/₈₄ × 554.4

= ^{115 × 554.4}/₈₄

= ⁶³⁷⁵⁶/₈₄ = 759

Thus, Sale Price to get a profit of 15% = $759 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) = $554.4

And, the loss = 16%

Then, the Sale Price (SP) to earn a profit of 15% = ?

Here, the Sale Price at a loss of 16 = $554.4

This means 84% of the Cost Price (CP) = 554.4

Therefore, 1% of the Cost Price (CP) = ^554.4/₈₄

Therefore, 100% of the Cost Price (CP)

= ^554.4/₈₄ × 100 = 660

Thus, the Cost Price (CP) = $660

Now, we need to find the Sale Price at a profit of 15%

Thus, Sale Price at a profit of 15%

= 115% of the Cost Price (CP)

= 115% of 660

= ¹¹⁵/₁₀₀ × 660 = 759

Thus, the Cost Price at a profit of 15% = $759 Answer

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