Profit And Loss
Math MCQs

Question :    Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

Correct Answer  6781.8

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) = $800.1

And, the loss = 79%

Then, the Sale Price (SP) to earn a profit of 78% = ?

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 – 79} × 800.1

= ¹⁰⁰/₂₁ × 800.1

= ^{100 × 800.1}/₂₁

= ⁸⁰⁰¹⁰/₂₁ = 3810

Thus, the Cost Price (CP) = $3810

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

Here now, CP = $3810

And, profit = 78%

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 + 78}/₁₀₀ × 3810

= ¹⁷⁸/₁₀₀ × 3810

= ^{178 × 3810}/₁₀₀

= ⁶⁷⁸¹⁸⁰/₁₀₀ = 6781.8

Thus, Sale Price (SP) at a profit of 78% = $6781.8 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) = $800.1

And, the loss = 79%

Then, the Sale Price (SP) to earn a profit of 78% = ?

Let the Cost Price (CP) = m

Here given loss = 79%

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

= 79% of m

= 79% × m

= ⁷⁹/₁₀₀ × m

⇒ loss = ^{79 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 800.1 = m – ^{79 m}/₁₀₀

⇒ 800.1 = ^{100 m – 79 m}/₁₀₀

⇒ 800.1 = ^{21 m}/₁₀₀

After cross multiplication, we get

800.1 × 100 = 21 m

⇒ 21 m = 800.1 × 100

⇒ m = ^{800.1 × 100}/₂₁

⇒ m = ⁸⁰⁰¹⁰/₂₁ = 3810

⇒ m = 3810

Thus, the Cost Price (CP) = $3810

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

Now, here, Cost Price = 3810

And, the profit = 78%

Thus, Sale Price (SP)

= Cost Price (CP) + 78% of Cost Price (CP)

= 3810 + ⁷⁸/₁₀₀ × 3810

= 3810 + ^{78 × 3810}/₁₀₀

= 3810 + ²⁹⁷¹⁸⁰/₁₀₀

= 3810 + 2971.8 = 6781.8

Thus, Sale Price (SP) at a profit of 78% = $6781.8 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) = $800.1

And, the loss = 79%

Then, the Sale Price (SP) to earn a profit of 78% = ?

Let, CP = 100

78% profit = 78% of CP

= 78% of 100 = 78

Thus, Sale Price to earn a profit of 78% = CP + 78

= 100 + 78 = 178

⇒ Sale Price to earn a profit of 78% = 178

79% loss = 79% of CP

= 79% of 100 = 79

Thus, Sale Price at a loss of 79% = CP – Loss

= 100 – 79 = 21

⇒ Sale Price at a loss of 79% = 21

∵ If the Sale Price is 21, then to earn a profit of 78% the Sale Price should be = 178

∴ If the Sale Price is 1, then to earn a profit of 78% the Sale Price should be

= ¹⁷⁸/₂₁

∴ If the Sale Price is 800.1, then to earn a profit of 78% the Sale Price should be

= ¹⁷⁸/₂₁ × 800.1

= ^{178 × 800.1}/₂₁

= ^142417.8/₂₁ = 6781.8

Thus, Sale Price to get a profit of 78% = $6781.8 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) = $800.1

And, the loss = 79%

Then, the Sale Price (SP) to earn a profit of 78% = ?

Here, the Sale Price at a loss of 79 = $800.1

This means 21% of the Cost Price (CP) = 800.1

Therefore, 1% of the Cost Price (CP) = ^800.1/₂₁

Therefore, 100% of the Cost Price (CP)

= ^800.1/₂₁ × 100 = 3810

Thus, the Cost Price (CP) = $3810

Now, we need to find the Sale Price at a profit of 78%

Thus, Sale Price at a profit of 78%

= 178% of the Cost Price (CP)

= 178% of 3810

= ¹⁷⁸/₁₀₀ × 3810 = 6781.8

Thus, the Cost Price at a profit of 78% = $6781.8 Answer

Similar Questions

(1) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

(2) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.

(3) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

(4) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?

(5) Find the cost price, if a trader gets a loss of 54% by selling 100 bags of mobile covers for $4880.60

(6) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

(7) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(8) Find the cost price, if a trader gets a loss of 57% by selling a TV set for $4820.30

(9) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(10) Find the cost price, if a trader gets a loss of 74% by selling 50 bags of rice for $3798.60