Profit And Loss
Math MCQs

Question :    Mr. James loses 24% after selling an article for $805.60. For how much should he sell it to get a profit of 23%?

Correct Answer  1303.8

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) = $805.6

And, the loss = 24%

Then, the Sale Price (SP) to earn a profit of 23% = ?

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 – 24} × 805.6

= ¹⁰⁰/₇₆ × 805.6

= ^{100 × 805.6}/₇₆

= ⁸⁰⁵⁶⁰/₇₆ = 1060

Thus, the Cost Price (CP) = $1060

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

Here now, CP = $1060

And, profit = 23%

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 + 23}/₁₀₀ × 1060

= ¹²³/₁₀₀ × 1060

= ^{123 × 1060}/₁₀₀

= ¹³⁰³⁸⁰/₁₀₀ = 1303.8

Thus, Sale Price (SP) at a profit of 23% = $1303.8 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) = $805.6

And, the loss = 24%

Then, the Sale Price (SP) to earn a profit of 23% = ?

Let the Cost Price (CP) = m

Here given loss = 24%

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

= 24% of m

= 24% × m

= ²⁴/₁₀₀ × m

⇒ loss = ^{24 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 805.6 = m – ^{24 m}/₁₀₀

⇒ 805.6 = ^{100 m – 24 m}/₁₀₀

⇒ 805.6 = ^{76 m}/₁₀₀

After cross multiplication, we get

805.6 × 100 = 76 m

⇒ 76 m = 805.6 × 100

⇒ m = ^{805.6 × 100}/₇₆

⇒ m = ⁸⁰⁵⁶⁰/₇₆ = 1060

⇒ m = 1060

Thus, the Cost Price (CP) = $1060

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

Now, here, Cost Price = 1060

And, the profit = 23%

Thus, Sale Price (SP)

= Cost Price (CP) + 23% of Cost Price (CP)

= 1060 + ²³/₁₀₀ × 1060

= 1060 + ^{23 × 1060}/₁₀₀

= 1060 + ²⁴³⁸⁰/₁₀₀

= 1060 + 243.8 = 1303.8

Thus, Sale Price (SP) at a profit of 23% = $1303.8 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) = $805.6

And, the loss = 24%

Then, the Sale Price (SP) to earn a profit of 23% = ?

Let, CP = 100

23% profit = 23% of CP

= 23% of 100 = 23

Thus, Sale Price to earn a profit of 23% = CP + 23

= 100 + 23 = 123

⇒ Sale Price to earn a profit of 23% = 123

24% loss = 24% of CP

= 24% of 100 = 24

Thus, Sale Price at a loss of 24% = CP – Loss

= 100 – 24 = 76

⇒ Sale Price at a loss of 24% = 76

∵ If the Sale Price is 76, then to earn a profit of 23% the Sale Price should be = 123

∴ If the Sale Price is 1, then to earn a profit of 23% the Sale Price should be

= ¹²³/₇₆

∴ If the Sale Price is 805.6, then to earn a profit of 23% the Sale Price should be

= ¹²³/₇₆ × 805.6

= ^{123 × 805.6}/₇₆

= ^99088.8/₇₆ = 1303.8

Thus, Sale Price to get a profit of 23% = $1303.8 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) = $805.6

And, the loss = 24%

Then, the Sale Price (SP) to earn a profit of 23% = ?

Here, the Sale Price at a loss of 24 = $805.6

This means 76% of the Cost Price (CP) = 805.6

Therefore, 1% of the Cost Price (CP) = ^805.6/₇₆

Therefore, 100% of the Cost Price (CP)

= ^805.6/₇₆ × 100 = 1060

Thus, the Cost Price (CP) = $1060

Now, we need to find the Sale Price at a profit of 23%

Thus, Sale Price at a profit of 23%

= 123% of the Cost Price (CP)

= 123% of 1060

= ¹²³/₁₀₀ × 1060 = 1303.8

Thus, the Cost Price at a profit of 23% = $1303.8 Answer

Similar Questions

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(2) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(3) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(4) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80

(5) Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.

(6) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

(7) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(8) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?

(9) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(10) Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.