Profit And Loss
Math MCQs

Question :    A dealer loses 28% by selling some articles for $907.20. For how much should he sell them to get a profit of 27%?

Correct Answer  1600.2

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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

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 – 28} × 907.2

= ¹⁰⁰/₇₂ × 907.2

= ^{100 × 907.2}/₇₂

= ⁹⁰⁷²⁰/₇₂ = 1260

Thus, the Cost Price (CP) = $1260

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

Here now, CP = $1260

And, profit = 27%

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 + 27}/₁₀₀ × 1260

= ¹²⁷/₁₀₀ × 1260

= ^{127 × 1260}/₁₀₀

= ¹⁶⁰⁰²⁰/₁₀₀ = 1600.2

Thus, Sale Price (SP) at a profit of 27% = $1600.2 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

Let the Cost Price (CP) = m

Here given loss = 28%

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

= 28% of m

= 28% × m

= ²⁸/₁₀₀ × m

⇒ loss = ^{28 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 907.2 = m – ^{28 m}/₁₀₀

⇒ 907.2 = ^{100 m – 28 m}/₁₀₀

⇒ 907.2 = ^{72 m}/₁₀₀

After cross multiplication, we get

907.2 × 100 = 72 m

⇒ 72 m = 907.2 × 100

⇒ m = ^{907.2 × 100}/₇₂

⇒ m = ⁹⁰⁷²⁰/₇₂ = 1260

⇒ m = 1260

Thus, the Cost Price (CP) = $1260

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

Now, here, Cost Price = 1260

And, the profit = 27%

Thus, Sale Price (SP)

= Cost Price (CP) + 27% of Cost Price (CP)

= 1260 + ²⁷/₁₀₀ × 1260

= 1260 + ^{27 × 1260}/₁₀₀

= 1260 + ³⁴⁰²⁰/₁₀₀

= 1260 + 340.2 = 1600.2

Thus, Sale Price (SP) at a profit of 27% = $1600.2 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

Let, CP = 100

27% profit = 27% of CP

= 27% of 100 = 27

Thus, Sale Price to earn a profit of 27% = CP + 27

= 100 + 27 = 127

⇒ Sale Price to earn a profit of 27% = 127

28% loss = 28% of CP

= 28% of 100 = 28

Thus, Sale Price at a loss of 28% = CP – Loss

= 100 – 28 = 72

⇒ Sale Price at a loss of 28% = 72

∵ If the Sale Price is 72, then to earn a profit of 27% the Sale Price should be = 127

∴ If the Sale Price is 1, then to earn a profit of 27% the Sale Price should be

= ¹²⁷/₇₂

∴ If the Sale Price is 907.2, then to earn a profit of 27% the Sale Price should be

= ¹²⁷/₇₂ × 907.2

= ^{127 × 907.2}/₇₂

= ^115214.4/₇₂ = 1600.2

Thus, Sale Price to get a profit of 27% = $1600.2 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) = $907.2

And, the loss = 28%

Then, the Sale Price (SP) to earn a profit of 27% = ?

Here, the Sale Price at a loss of 28 = $907.2

This means 72% of the Cost Price (CP) = 907.2

Therefore, 1% of the Cost Price (CP) = ^907.2/₇₂

Therefore, 100% of the Cost Price (CP)

= ^907.2/₇₂ × 100 = 1260

Thus, the Cost Price (CP) = $1260

Now, we need to find the Sale Price at a profit of 27%

Thus, Sale Price at a profit of 27%

= 127% of the Cost Price (CP)

= 127% of 1260

= ¹²⁷/₁₀₀ × 1260 = 1600.2

Thus, the Cost Price at a profit of 27% = $1600.2 Answer

Similar Questions

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(3) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

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(7) If a peddler bought 71 paper clips for $1 and sold 70 paper clips for $1 then, find the profit in percent.

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