Profit And Loss
Math MCQs

Question :    A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?

Correct Answer  3815.2

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) = $1179.7

And, the loss = 53%

Then, the Sale Price (SP) to earn a profit of 52% = ?

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 – 53} × 1179.7

= ¹⁰⁰/₄₇ × 1179.7

= ^{100 × 1179.7}/₄₇

= ¹¹⁷⁹⁷⁰/₄₇ = 2510

Thus, the Cost Price (CP) = $2510

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

Here now, CP = $2510

And, profit = 52%

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 + 52}/₁₀₀ × 2510

= ¹⁵²/₁₀₀ × 2510

= ^{152 × 2510}/₁₀₀

= ³⁸¹⁵²⁰/₁₀₀ = 3815.2

Thus, Sale Price (SP) at a profit of 52% = $3815.2 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) = $1179.7

And, the loss = 53%

Then, the Sale Price (SP) to earn a profit of 52% = ?

Let the Cost Price (CP) = m

Here given loss = 53%

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

= 53% of m

= 53% × m

= ⁵³/₁₀₀ × m

⇒ loss = ^{53 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1179.7 = m – ^{53 m}/₁₀₀

⇒ 1179.7 = ^{100 m – 53 m}/₁₀₀

⇒ 1179.7 = ^{47 m}/₁₀₀

After cross multiplication, we get

1179.7 × 100 = 47 m

⇒ 47 m = 1179.7 × 100

⇒ m = ^{1179.7 × 100}/₄₇

⇒ m = ¹¹⁷⁹⁷⁰/₄₇ = 2510

⇒ m = 2510

Thus, the Cost Price (CP) = $2510

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

Now, here, Cost Price = 2510

And, the profit = 52%

Thus, Sale Price (SP)

= Cost Price (CP) + 52% of Cost Price (CP)

= 2510 + ⁵²/₁₀₀ × 2510

= 2510 + ^{52 × 2510}/₁₀₀

= 2510 + ¹³⁰⁵²⁰/₁₀₀

= 2510 + 1305.2 = 3815.2

Thus, Sale Price (SP) at a profit of 52% = $3815.2 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) = $1179.7

And, the loss = 53%

Then, the Sale Price (SP) to earn a profit of 52% = ?

Let, CP = 100

52% profit = 52% of CP

= 52% of 100 = 52

Thus, Sale Price to earn a profit of 52% = CP + 52

= 100 + 52 = 152

⇒ Sale Price to earn a profit of 52% = 152

53% loss = 53% of CP

= 53% of 100 = 53

Thus, Sale Price at a loss of 53% = CP – Loss

= 100 – 53 = 47

⇒ Sale Price at a loss of 53% = 47

∵ If the Sale Price is 47, then to earn a profit of 52% the Sale Price should be = 152

∴ If the Sale Price is 1, then to earn a profit of 52% the Sale Price should be

= ¹⁵²/₄₇

∴ If the Sale Price is 1179.7, then to earn a profit of 52% the Sale Price should be

= ¹⁵²/₄₇ × 1179.7

= ^{152 × 1179.7}/₄₇

= ^179314.4/₄₇ = 3815.2

Thus, Sale Price to get a profit of 52% = $3815.2 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) = $1179.7

And, the loss = 53%

Then, the Sale Price (SP) to earn a profit of 52% = ?

Here, the Sale Price at a loss of 53 = $1179.7

This means 47% of the Cost Price (CP) = 1179.7

Therefore, 1% of the Cost Price (CP) = ^1179.7/₄₇

Therefore, 100% of the Cost Price (CP)

= ^1179.7/₄₇ × 100 = 2510

Thus, the Cost Price (CP) = $2510

Now, we need to find the Sale Price at a profit of 52%

Thus, Sale Price at a profit of 52%

= 152% of the Cost Price (CP)

= 152% of 2510

= ¹⁵²/₁₀₀ × 2510 = 3815.2

Thus, the Cost Price at a profit of 52% = $3815.2 Answer

Similar Questions

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(2) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

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(5) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

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(7) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(8) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(9) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

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