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

(3) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(4) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

(5) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(6) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

(7) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.

(8) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.

(9) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(10) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.