Profit And Loss
Math MCQs

Question :    A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?

Correct Answer  3132

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) = $1166.4

And, the loss = 46%

Then, the Sale Price (SP) to earn a profit of 45% = ?

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 – 46} × 1166.4

= ¹⁰⁰/₅₄ × 1166.4

= ^{100 × 1166.4}/₅₄

= ¹¹⁶⁶⁴⁰/₅₄ = 2160

Thus, the Cost Price (CP) = $2160

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

Here now, CP = $2160

And, profit = 45%

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 + 45}/₁₀₀ × 2160

= ¹⁴⁵/₁₀₀ × 2160

= ^{145 × 2160}/₁₀₀

= ³¹³²⁰⁰/₁₀₀ = 3132

Thus, Sale Price (SP) at a profit of 45% = $3132 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) = $1166.4

And, the loss = 46%

Then, the Sale Price (SP) to earn a profit of 45% = ?

Let the Cost Price (CP) = m

Here given loss = 46%

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

= 46% of m

= 46% × m

= ⁴⁶/₁₀₀ × m

⇒ loss = ^{46 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1166.4 = m – ^{46 m}/₁₀₀

⇒ 1166.4 = ^{100 m – 46 m}/₁₀₀

⇒ 1166.4 = ^{54 m}/₁₀₀

After cross multiplication, we get

1166.4 × 100 = 54 m

⇒ 54 m = 1166.4 × 100

⇒ m = ^{1166.4 × 100}/₅₄

⇒ m = ¹¹⁶⁶⁴⁰/₅₄ = 2160

⇒ m = 2160

Thus, the Cost Price (CP) = $2160

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

Now, here, Cost Price = 2160

And, the profit = 45%

Thus, Sale Price (SP)

= Cost Price (CP) + 45% of Cost Price (CP)

= 2160 + ⁴⁵/₁₀₀ × 2160

= 2160 + ^{45 × 2160}/₁₀₀

= 2160 + ⁹⁷²⁰⁰/₁₀₀

= 2160 + 972 = 3132

Thus, Sale Price (SP) at a profit of 45% = $3132 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) = $1166.4

And, the loss = 46%

Then, the Sale Price (SP) to earn a profit of 45% = ?

Let, CP = 100

45% profit = 45% of CP

= 45% of 100 = 45

Thus, Sale Price to earn a profit of 45% = CP + 45

= 100 + 45 = 145

⇒ Sale Price to earn a profit of 45% = 145

46% loss = 46% of CP

= 46% of 100 = 46

Thus, Sale Price at a loss of 46% = CP – Loss

= 100 – 46 = 54

⇒ Sale Price at a loss of 46% = 54

∵ If the Sale Price is 54, then to earn a profit of 45% the Sale Price should be = 145

∴ If the Sale Price is 1, then to earn a profit of 45% the Sale Price should be

= ¹⁴⁵/₅₄

∴ If the Sale Price is 1166.4, then to earn a profit of 45% the Sale Price should be

= ¹⁴⁵/₅₄ × 1166.4

= ^{145 × 1166.4}/₅₄

= ¹⁶⁹¹²⁸/₅₄ = 3132

Thus, Sale Price to get a profit of 45% = $3132 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) = $1166.4

And, the loss = 46%

Then, the Sale Price (SP) to earn a profit of 45% = ?

Here, the Sale Price at a loss of 46 = $1166.4

This means 54% of the Cost Price (CP) = 1166.4

Therefore, 1% of the Cost Price (CP) = ^1166.4/₅₄

Therefore, 100% of the Cost Price (CP)

= ^1166.4/₅₄ × 100 = 2160

Thus, the Cost Price (CP) = $2160

Now, we need to find the Sale Price at a profit of 45%

Thus, Sale Price at a profit of 45%

= 145% of the Cost Price (CP)

= 145% of 2160

= ¹⁴⁵/₁₀₀ × 2160 = 3132

Thus, the Cost Price at a profit of 45% = $3132 Answer

Similar Questions

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(2) A trader gets a loss of 52% by selling 500 bags of rice for $4900.80. Find the cost price of rice.

(3) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?

(4) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?

(5) If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

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