Profit And Loss
Math MCQs

Question :    A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

Correct Answer  392.4

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) = $324

And, the loss = 10%

Then, the Sale Price (SP) to earn a profit of 9% = ?

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 – 10} × 324

= ¹⁰⁰/₉₀ × 324

= ^{100 × 324}/₉₀

= ³²⁴⁰⁰/₉₀ = 360

Thus, the Cost Price (CP) = $360

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

Here now, CP = $360

And, profit = 9%

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 + 9}/₁₀₀ × 360

= ¹⁰⁹/₁₀₀ × 360

= ^{109 × 360}/₁₀₀

= ³⁹²⁴⁰/₁₀₀ = 392.4

Thus, Sale Price (SP) at a profit of 9% = $392.4 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) = $324

And, the loss = 10%

Then, the Sale Price (SP) to earn a profit of 9% = ?

Let the Cost Price (CP) = m

Here given loss = 10%

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

= 10% of m

= 10% × m

= ¹⁰/₁₀₀ × m

⇒ loss = ^{10 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 324 = m – ^{10 m}/₁₀₀

⇒ 324 = ^{100 m – 10 m}/₁₀₀

⇒ 324 = ^{90 m}/₁₀₀

After cross multiplication, we get

324 × 100 = 90 m

⇒ 90 m = 324 × 100

⇒ m = ^{324 × 100}/₉₀

⇒ m = ³²⁴⁰⁰/₉₀ = 360

⇒ m = 360

Thus, the Cost Price (CP) = $360

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

Now, here, Cost Price = 360

And, the profit = 9%

Thus, Sale Price (SP)

= Cost Price (CP) + 9% of Cost Price (CP)

= 360 + ⁹/₁₀₀ × 360

= 360 + ^{9 × 360}/₁₀₀

= 360 + ³²⁴⁰/₁₀₀

= 360 + 32.4 = 392.4

Thus, Sale Price (SP) at a profit of 9% = $392.4 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) = $324

And, the loss = 10%

Then, the Sale Price (SP) to earn a profit of 9% = ?

Let, CP = 100

9% profit = 9% of CP

= 9% of 100 = 9

Thus, Sale Price to earn a profit of 9% = CP + 9

= 100 + 9 = 109

⇒ Sale Price to earn a profit of 9% = 109

10% loss = 10% of CP

= 10% of 100 = 10

Thus, Sale Price at a loss of 10% = CP – Loss

= 100 – 10 = 90

⇒ Sale Price at a loss of 10% = 90

∵ If the Sale Price is 90, then to earn a profit of 9% the Sale Price should be = 109

∴ If the Sale Price is 1, then to earn a profit of 9% the Sale Price should be

= ¹⁰⁹/₉₀

∴ If the Sale Price is 324, then to earn a profit of 9% the Sale Price should be

= ¹⁰⁹/₉₀ × 324

= ^{109 × 324}/₉₀

= ³⁵³¹⁶/₉₀ = 392.4

Thus, Sale Price to get a profit of 9% = $392.4 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) = $324

And, the loss = 10%

Then, the Sale Price (SP) to earn a profit of 9% = ?

Here, the Sale Price at a loss of 10 = $324

This means 90% of the Cost Price (CP) = 324

Therefore, 1% of the Cost Price (CP) = ³²⁴/₉₀

Therefore, 100% of the Cost Price (CP)

= ³²⁴/₉₀ × 100 = 360

Thus, the Cost Price (CP) = $360

Now, we need to find the Sale Price at a profit of 9%

Thus, Sale Price at a profit of 9%

= 109% of the Cost Price (CP)

= 109% of 360

= ¹⁰⁹/₁₀₀ × 360 = 392.4

Thus, the Cost Price at a profit of 9% = $392.4 Answer

Similar Questions

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(2) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.

(3) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?

(4) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?

(5) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

(6) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10

(7) The cost price of an article is $15 and the sale price is $20, then find the profit and profit percent.

(8) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(9) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

(10) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.