Profit And Loss
Math MCQs

Question :    A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?

Correct Answer  1754.4

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) = $952

And, the loss = 30%

Then, the Sale Price (SP) to earn a profit of 29% = ?

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 – 30} × 952

= ¹⁰⁰/₇₀ × 952

= ^{100 × 952}/₇₀

= ⁹⁵²⁰⁰/₇₀ = 1360

Thus, the Cost Price (CP) = $1360

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

Here now, CP = $1360

And, profit = 29%

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 + 29}/₁₀₀ × 1360

= ¹²⁹/₁₀₀ × 1360

= ^{129 × 1360}/₁₀₀

= ¹⁷⁵⁴⁴⁰/₁₀₀ = 1754.4

Thus, Sale Price (SP) at a profit of 29% = $1754.4 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) = $952

And, the loss = 30%

Then, the Sale Price (SP) to earn a profit of 29% = ?

Let the Cost Price (CP) = m

Here given loss = 30%

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

= 30% of m

= 30% × m

= ³⁰/₁₀₀ × m

⇒ loss = ^{30 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 952 = m – ^{30 m}/₁₀₀

⇒ 952 = ^{100 m – 30 m}/₁₀₀

⇒ 952 = ^{70 m}/₁₀₀

After cross multiplication, we get

952 × 100 = 70 m

⇒ 70 m = 952 × 100

⇒ m = ^{952 × 100}/₇₀

⇒ m = ⁹⁵²⁰⁰/₇₀ = 1360

⇒ m = 1360

Thus, the Cost Price (CP) = $1360

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

Now, here, Cost Price = 1360

And, the profit = 29%

Thus, Sale Price (SP)

= Cost Price (CP) + 29% of Cost Price (CP)

= 1360 + ²⁹/₁₀₀ × 1360

= 1360 + ^{29 × 1360}/₁₀₀

= 1360 + ³⁹⁴⁴⁰/₁₀₀

= 1360 + 394.4 = 1754.4

Thus, Sale Price (SP) at a profit of 29% = $1754.4 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) = $952

And, the loss = 30%

Then, the Sale Price (SP) to earn a profit of 29% = ?

Let, CP = 100

29% profit = 29% of CP

= 29% of 100 = 29

Thus, Sale Price to earn a profit of 29% = CP + 29

= 100 + 29 = 129

⇒ Sale Price to earn a profit of 29% = 129

30% loss = 30% of CP

= 30% of 100 = 30

Thus, Sale Price at a loss of 30% = CP – Loss

= 100 – 30 = 70

⇒ Sale Price at a loss of 30% = 70

∵ If the Sale Price is 70, then to earn a profit of 29% the Sale Price should be = 129

∴ If the Sale Price is 1, then to earn a profit of 29% the Sale Price should be

= ¹²⁹/₇₀

∴ If the Sale Price is 952, then to earn a profit of 29% the Sale Price should be

= ¹²⁹/₇₀ × 952

= ^{129 × 952}/₇₀

= ¹²²⁸⁰⁸/₇₀ = 1754.4

Thus, Sale Price to get a profit of 29% = $1754.4 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) = $952

And, the loss = 30%

Then, the Sale Price (SP) to earn a profit of 29% = ?

Here, the Sale Price at a loss of 30 = $952

This means 70% of the Cost Price (CP) = 952

Therefore, 1% of the Cost Price (CP) = ⁹⁵²/₇₀

Therefore, 100% of the Cost Price (CP)

= ⁹⁵²/₇₀ × 100 = 1360

Thus, the Cost Price (CP) = $1360

Now, we need to find the Sale Price at a profit of 29%

Thus, Sale Price at a profit of 29%

= 129% of the Cost Price (CP)

= 129% of 1360

= ¹²⁹/₁₀₀ × 1360 = 1754.4

Thus, the Cost Price at a profit of 29% = $1754.4 Answer

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