Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

Correct Answer  7710

Solution & Explanation

Solution

Finding the cost price if the sale price and profit percent are known

The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.

Finding the cost price using the formula when the sale price and profit percent are known

Given, the sale price (SP) = $37779

And, the profit = 390%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and profit percent are known

Cost Price (CP) = ¹⁰⁰/_{100 + gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 + 390} × 37779

= ^{100 × 37779}/₄₉₀

= ^3777900/₄₉₀ = 7710

Thus, the Cost Price (CP) = $7710 Answer

Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given

Let the Cost Price (CP) = m

Here given profit = 390%

Calculation of Profit

Profit is calculated on cost price (CP)

Formula to find the Profit = Profit% of CP

Thus, profit on the cost price of m

= 390% of m

= 390% × m

= ³⁹⁰/₁₀₀ × m

⇒ Profit = ^{390 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 37779 = m + ^{390 m}/₁₀₀

⇒ 37779 = ^{100 m + 390 m}/₁₀₀

⇒ 37779 = ^{490 m}/₁₀₀

After cross multiplication, we get

37779 × 100 = 490 m

⇒ 490 m = 37779 × 100

⇒ m = ^{37779 × 100}/₄₉₀

⇒ m = ^3777900/₄₉₀ = 7710

⇒ m = 7710

Thus, the Cost Price (CP) = $7710 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given

Given, the sale price (SP) = $37779

And, the profit = 390%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 390% of 100 = 390

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 390

⇒ Sale Price (SP) = 490

∵ If the Sale Price (SP) is 490, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₄₉₀

∴ If the Sale Price (SP) is 37779, then the Cost Price (CP)

= ¹⁰⁰/₄₉₀ × 37779

= ^{100 × 37779}/₄₉₀

= ^3777900/₄₉₀ = 7710

Thus, the Cost Price (CP) = $7710 Answer

Shortcut Method to find Cost Price (CP) when SP and profit percent are known

Given, the sale price (SP) = $37779

And, the profit = 390%

Then, the Cost Price (CP) = ?

SP = 490% of CP

⇒ SP = ⁴⁹⁰/₁₀₀ × CP

⇒ 37779 = ^{490 CP}/₁₀₀

After cross multiplication

⇒ 37779 × 100 = 490 CP

⇒ 490 CP = 37779 × 100

⇒ CP = ^{37779 × 100}/₄₉₀

⇒ CP = ^3777900/₄₉₀ = 7710

⇒ CP = $7710 Answer

Similar Questions

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(9) Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?

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