Profit And Loss
Math MCQs

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

Correct Answer  1910

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) = $3820

And, the profit = 100%

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 + 100} × 3820

= ^{100 × 3820}/₂₀₀

= ³⁸²⁰⁰⁰/₂₀₀ = 1910

Thus, the Cost Price (CP) = $1910 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 = 100%

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

= 100% of m

= 100% × m

= ¹⁰⁰/₁₀₀ × m

⇒ Profit = ^{100 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 3820 = m + ^{100 m}/₁₀₀

⇒ 3820 = ^{100 m + 100 m}/₁₀₀

⇒ 3820 = ^{200 m}/₁₀₀

After cross multiplication, we get

3820 × 100 = 200 m

⇒ 200 m = 3820 × 100

⇒ m = ^{3820 × 100}/₂₀₀

⇒ m = ³⁸²⁰⁰⁰/₂₀₀ = 1910

⇒ m = 1910

Thus, the Cost Price (CP) = $1910 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) = $3820

And, the profit = 100%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 100% of 100 = 100

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

⇒ Sale Price (SP) = 100 + 100

⇒ Sale Price (SP) = 200

∵ If the Sale Price (SP) is 200, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₀₀

∴ If the Sale Price (SP) is 3820, then the Cost Price (CP)

= ¹⁰⁰/₂₀₀ × 3820

= ^{100 × 3820}/₂₀₀

= ³⁸²⁰⁰⁰/₂₀₀ = 1910

Thus, the Cost Price (CP) = $1910 Answer

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

Given, the sale price (SP) = $3820

And, the profit = 100%

Then, the Cost Price (CP) = ?

SP = 200% of CP

⇒ SP = ²⁰⁰/₁₀₀ × CP

⇒ 3820 = ^{200 CP}/₁₀₀

After cross multiplication

⇒ 3820 × 100 = 200 CP

⇒ 200 CP = 3820 × 100

⇒ CP = ^{3820 × 100}/₂₀₀

⇒ CP = ³⁸²⁰⁰⁰/₂₀₀ = 1910

⇒ CP = $1910 Answer

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