Profit And Loss
Math MCQs

Question :    Mr. Henry loses 26% by selling an article for $858.4. For how much should he sell it to get a profit of 25%?

Correct Answer  1450

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) = $858.4

And, the loss = 26%

Then, the Sale Price (SP) to earn a profit of 25% = ?

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 – 26} × 858.4

= ¹⁰⁰/₇₄ × 858.4

= ^{100 × 858.4}/₇₄

= ⁸⁵⁸⁴⁰/₇₄ = 1160

Thus, the Cost Price (CP) = $1160

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

Here now, CP = $1160

And, profit = 25%

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 + 25}/₁₀₀ × 1160

= ¹²⁵/₁₀₀ × 1160

= ^{125 × 1160}/₁₀₀

= ¹⁴⁵⁰⁰⁰/₁₀₀ = 1450

Thus, Sale Price (SP) at a profit of 25% = $1450 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) = $858.4

And, the loss = 26%

Then, the Sale Price (SP) to earn a profit of 25% = ?

Let the Cost Price (CP) = m

Here given loss = 26%

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

= 26% of m

= 26% × m

= ²⁶/₁₀₀ × m

⇒ loss = ^{26 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 858.4 = m – ^{26 m}/₁₀₀

⇒ 858.4 = ^{100 m – 26 m}/₁₀₀

⇒ 858.4 = ^{74 m}/₁₀₀

After cross multiplication, we get

858.4 × 100 = 74 m

⇒ 74 m = 858.4 × 100

⇒ m = ^{858.4 × 100}/₇₄

⇒ m = ⁸⁵⁸⁴⁰/₇₄ = 1160

⇒ m = 1160

Thus, the Cost Price (CP) = $1160

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

Now, here, Cost Price = 1160

And, the profit = 25%

Thus, Sale Price (SP)

= Cost Price (CP) + 25% of Cost Price (CP)

= 1160 + ²⁵/₁₀₀ × 1160

= 1160 + ^{25 × 1160}/₁₀₀

= 1160 + ²⁹⁰⁰⁰/₁₀₀

= 1160 + 290 = 1450

Thus, Sale Price (SP) at a profit of 25% = $1450 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) = $858.4

And, the loss = 26%

Then, the Sale Price (SP) to earn a profit of 25% = ?

Let, CP = 100

25% profit = 25% of CP

= 25% of 100 = 25

Thus, Sale Price to earn a profit of 25% = CP + 25

= 100 + 25 = 125

⇒ Sale Price to earn a profit of 25% = 125

26% loss = 26% of CP

= 26% of 100 = 26

Thus, Sale Price at a loss of 26% = CP – Loss

= 100 – 26 = 74

⇒ Sale Price at a loss of 26% = 74

∵ If the Sale Price is 74, then to earn a profit of 25% the Sale Price should be = 125

∴ If the Sale Price is 1, then to earn a profit of 25% the Sale Price should be

= ¹²⁵/₇₄

∴ If the Sale Price is 858.4, then to earn a profit of 25% the Sale Price should be

= ¹²⁵/₇₄ × 858.4

= ^{125 × 858.4}/₇₄

= ¹⁰⁷³⁰⁰/₇₄ = 1450

Thus, Sale Price to get a profit of 25% = $1450 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) = $858.4

And, the loss = 26%

Then, the Sale Price (SP) to earn a profit of 25% = ?

Here, the Sale Price at a loss of 26 = $858.4

This means 74% of the Cost Price (CP) = 858.4

Therefore, 1% of the Cost Price (CP) = ^858.4/₇₄

Therefore, 100% of the Cost Price (CP)

= ^858.4/₇₄ × 100 = 1160

Thus, the Cost Price (CP) = $1160

Now, we need to find the Sale Price at a profit of 25%

Thus, Sale Price at a profit of 25%

= 125% of the Cost Price (CP)

= 125% of 1160

= ¹²⁵/₁₀₀ × 1160 = 1450

Thus, the Cost Price at a profit of 25% = $1450 Answer

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